Hi, Lloyd. I'm not quite certain where to begin regarding your question, but I'll keep it to DNA matters only, and I'll have a couple of questions for you, as well. The first of these:
"I have talked to several experts and they advise for very good reason to NEVER use the TIP feature."
What experts have you spoken with? The FTDNA TiP feature, while imperfect, is not atrociously so. My biggest difficulty with it has always been the number of significant digits used for its presentation of possible generations-to-MRCA. I would prefer to see the percentages rounded: carrying them out to 1/100th of a percent implies a precision that simply isn't possible.
"The proper way is to say that a GD-0, GD-1, GD-2 and GD-3 will match within a range..."
Which is what the TiP utility does, while comparing two sets of data and making some allowances for individual marker mutation rates. But you may have been led to believe that all estimations of genetic distance are equivalent. They're aren't. Not only is there more than one model for arriving at genetic distance for Y-STRs (FTDNA switched to the infinite allele model in summer 2016), but in the two decades that we've been recording and compiling Y-STR mutation rate data--and continue to do so--we've learned that individual markers differ from each other by as much as a factor of magnitude in the observed average mutation rates.
For example, the palindromic marker CDY is perhaps the most notorious for being volatile and fast-moving. Some observed mutation rates have placed it as high as 0.0353 per generation. The slowest marker I've seen so far is DYS632, estimated to have a 0.00007 mutation rate per generation. Yet a copy count difference of one at either of those markers would constitute a GD of 1. In this regard, TiP actually does a mediocre to fair job, given the complexities. I have frequently compared STR marker data side by side and seen equivalent genetic distances evaluated differently by TiP as confidence-to-MRCA based on which STR markers differed, which is the only accurate way to approach such gross estimations.
"Quite clearly strong documentary evidence will always supersede the calculation for the reasons, particularly when the intersection is found in less than the the outer range shown and a GD-3 is as good as a GD-1 in these cases simply because mutations are entirely random."
For genealogy, DNA evidence of any type always has to work in lockstep with the paper-trail. The closest we can come to DNA serving as evidence sans paper-trail are the autosomal results of twins, parents/children, and full siblings. That said, the blanket statement that a Y-STR genetic distance of 3 is as good as 1 based only on the paper-trail simply cannot be made.
First, like anything else, the evidence has to be closely evaluated and--both a benefit and drawback of yDNA, being male-specific, haploidy, and escaping crossover--yDNA data easily reaches back into timeframes beyond any genealogical evidence. Second, any summary of genetic distance can only be considered against the number of markers tested. A GD of 3 at 37 markers can be vastly different than a GD of 3 at 111 markers: the two individuals might in fact be GD0 at 25 and 37 markers, and the differences only appear after DYS438 or even DYS565. For example, 25 STR markers are commonly used to determine possible descendancy from Niall of the Nine Hostages. A GD of 1 among those 25 markers has markedly more impact than does a cousin to me who is a GD of 1 at 111 markers at the relatively fast-moving DYS710.
I'm assisting right now with one group of five matches where the earliest known ancestor from one of the trees shows as born c. 1705. They had a paper-trail hypothesis about how four of the five lines connected. The results indicated that two of the lines probably converge earlier than thought, and the two lines thought to have the most consistent paper-trail were off by at least two generations to their MRCA, who now looks to have been born in the mid-1600s or earlier. To do a reasonable job in a comparison for that purpose requires use of phylogram modeling: you have to try to understand which mutations happened in what order framed against the paternal-line chart. Rare occurrences like recLOH events and back-mutations aside, developing that sort of dynamic model--using the actual mutations weighted for individual mutation rate probabilities--is really the only way to arrive at a more granular look at the picture than the high-level grouping in DNA projects or the overview of generations-to-MRCA that TiP provides.
An aside: Y-STR mutations are not entirely random. The aforementioned recLOH events is one example, as are certain null values and copy counts more common to some haplogroups than others, and the propensity of DYS464 to see additive or subtractive multiples. Markers also vary in copy-count diversity. For example, DYS454 will always have a repeat count of either 10, 11, or 12; DYS464 will typically contain four to eight copies, or sub-markers, each of which can range from 9 copies to 20 copies. Some markers simply have more room to move than others.
Speaking of the haplogroup, unless we're talking NextGen Y-chromosome full sequencing, really the only thing a haplogroup is genealogically useful for is negating the possibility of two men sharing a common ancestor. A matching haplogroup--yDNA or mtDNA--at any clade or high-level subclade is zero evidence of relatedness in the genealogical timeframe. Not long ago I had communications regarding someone who was adamant that his tested SNP of M222 was "proof" of descendancy from a minor branch of English royalty...never mind that M222 bifurcated from DF23 sometime around 4,500-3,900 YBP and pre-dates any English genealogy by at least a millennium. Oh, and a note that without specific Y-SNP testing, Y-STR values can only predict a haplogroup; they do that well at high levels, but not definitively. And that prediction can't be assumed to be refined via STR matching; in other words, if my predicted haplogroup is, say, DF29, or I1a, I can't presume I am deeper in the phylotree, at Z74, only because I have an STR match to someone who did have SNPs tested to that level.
"While exact reasons for mutation vary, I have noted among those who migrate considerably from the originating ancestor seem to mutate more often than those who remained stationary."
Do you have any sources of empirical data for that? I've been at this for a fair number of years and have never heard of any correlation between geography and Y-STR mutation rates. Age of the father at conception of the son, yes; but not geography.
To some it up, without detailed evaluation like phylogram modeling, TiP does a reasonable job for the constraints it has. For a snapshot overview, it's about the best we have. To simply look at a comparison by genetic distance only, without consideration for which markers may have mutated, we can view FTDNA's charts for 37 markers, 67 markers, and 111 markers. Considering Y-STR matching that way is mostly useless to genealogists unless dealing with GD0 or GD1. For example, for GD3 at 37 markers, we see that the two males are related, but the most it can be tightened down is: "The relationship is likely within the range of most well-established surname lineages in Western Europe." If a paper-trail shows a much closer TMRCA than would be indicated by the TiP report, close scrutiny of both the DNA and the paper-trail is called for.