Some indirect work that I think will be required for a good understanding of the Indo-Uralic question. In approximate descending order of usefulness, as I see it.
- Fully accounting for family-internal data on both sides.
- On the IE side, I understand this most pressingly means crafting a well-stratified model that separates Early PIE, Late PIE and intermediates.
- On the Uralic side, we are lacking no less than fully bridging Mari, Permic and Ugric with the standard model of PU rooted in the comparision of West Uralic with Proto-Samoyedic. Loanword studies, involving a deeper look at Iranian, Tocharian & substrates in Central Russia, may be necessary to weed out some junk.
- A coherent model of the interaction of PIE and pre-PIE with its known neighbors & likely contact languages: Semitic, Tyrsenian, all four Caucasian families (incl. Hurro-Urartian), possibly Sumerian and Burushaski.
- This in turn will ultimately require getting the reconstruction of NW and NE Caucasian into a useful state (and determining how viable uniting these as North Caucasian would be).
- Similarly, an analysis of possible old Altaic and Yeniseian contact influence in (pre-)Uralic.
- This also in turn needs a good reconstruction of those families. IIUC Common Turkic, Common Mongolian and Proto-Tungusic are in decent shape, but Proto-Turkic (= CT + Oghur) still needs work, and the Yeniseian data might be too scanty to allow resolving disputes between the Vajda and Starostin approaches.
- Assessing the "Uralo-Yukaghir" question, probably best done in relation to the previous (there is likely room for feedback from any improved understanding of Proto-Tungusic). Yukaghir seems unlikely to provide novel data, but might come useful for confirming a PU or pre-Uralic pedigree for various things.
- Working out the prehistory of the Bering Strait families & seeing if any salvageable "Uralo-Siberian" emerges. Again IIUC, not even Eskimo-Aleut proper has yet been reconstructed in detail.
Altogether: as I see it, these issues imply that tackling the Indo-Uralic question (or Eurasiatic in more general) head-on, while possible to try, is currently going to be riddled with red herrings, dead ends, and re-evaluations in wake of new results on the established families.
As noted by Allan Bomhard, we are all amateurs on Nostratic. No wonder, when it's this easy to list several related difficulties even for the "most promising" subcomponent of the hypothesis.
(I am of course implying that these issues lead to the discipline being treated as a pipe dream by institutions, not that they would entirely preclude concepts such as 'degree in Nostratics'.)
What's more though: these more or less integrally related issues are not casual language hobbyist territory. In this sense there is a very real possibility of entering an official a "Nostratics program": it just needs to be called something else. Any single entry could well support a linguist's whole career. Currently, dedicated amateurs can also still contribute valuable work on these - but, I would argue, not without having a good understanding on the greater academic context, and the intermediate and more distant goals at hand. If Nostratic could be solved by a single dedicated individual, it would have been done by now. The problem is clearly of a different caliber and calls for a well-connected network of scholars.
I understand most people interested in the subject have been mainly concerned on issues 1a & parts of 2 (the reconstruction of Early PIE and pre-PIE). I'm meanwhile mainly coming in from angle 1b (fortifying Proto-Uralic). Sometime in the indeterminate future (could be five years, could be fifty), issues 3 & 4 are what I would see as my next priority on the subject: both as topics to look into myself, and as topics on which to connect to the greater historical linguistics community.
Scholars up-to-date on modern Altaic or Caucasian studies would be also valuable here, and #5 probably needs serious work from someone other than Fortescue eventually.
And this all is of course only the northern and western reaches of "Nostratic"! Tackling Afro-Asiatic alone would call for a whole additional team of skilled linguists, and then there are the questions of Altaic unity, the factoring in of Dravidian & Kartvelian, etc.
In conclusion: anyone wishing to make tangible progress of questions of macro-comparison needs to remain patient, connected, and not spread oneself too thin.