...There are different tundra transmission used with the the JF1A transfer case, the AB60F, A750F and the A760F. Curious some vehicle VIN plates show the A760H transmission, but it's impossible too find these on toyodiy.com. The part number 35010-0C350 on the transmission does not exist there. It shows only the 35000-0C300 for the A760F one.
However the part numbers for the transfer case differ. Same for the input shafts. So I think there are different input shafts depending on engine and transmission configuration. Maybe some with 23 splines (AB60F?) and hopefully some with 19 splines (A750F, A760F/H?).
But I don't know, everything only guesswork.
So, I've been puzzling over your post for several days now, and frankly, I don't understand it. I'm beginning to think this is really a "what if" brain-storm project for your entertainment, with someone else doing the legwork.
What year is your Hilux, and what is the market value?...Does this mod make any sense economically? It probably doesn't make any sense for fuel savings, not even in Europe.
Do you already own an LS600h donor vehicle? If not, have you priced one?
I am not clear on why it has to be JF1A/JF3A transfer case and an A760 transmission...Does the LS600h donor vehicle have an A760H transmission? Forgetting about the output shaft splines, will a JF1A or JF3A transfer case even flange up to an A760H transmission? (Maybe you've already answered these questions for yourself, and it's not necessary to tell us.)
What I have been able to determine in research for you:
(1) Yes, you are correct. A search for A760H transmission on Toyota online dealer sites turns up "No records". You don't suppose this is exclusively a Lexus transmission? From my experience, Lexus part numbers, if they are exclusive to Lexus vehicles, will not show up on Toyota sites. Now, if the part is used on both vehicle brands, and that does happen, only the Toyota applications will show up on Toyota sites.
Edit: I can't reconfirm how I made the connection between the JF1A transfer case type and the part number below...the information below may be bogus. Sorry.
(2) The JF1A transfer case is used in 2010-2012 Sequoias, 2010-2017 Tundras with 4.6L 4WD (and maybe others, not an exhaustive search). It is available through Toyota online dealers with different part numbers for the applications (14-17 Tundra SR5: 36100-0C010) for about $2258, cheaper used through eBay ($500; shift actuator typically sold separately, maybe another $300).
(3) Your best bet for "spline counting" will likely be a retrofit dealer or a salvage dealer that has something to possibly gain from answering your questions. Most of us here only own one personal Tundra, and if we've had the pleasure of repairing the transfer case, we probably didn't count the splines in our haste to get it back together.
For example, my research shows that earlier Tundra, 4.7L 4WD transfer cases (PN 36110-34010) could very well have 19 splines from a count/estimate of a magnified eBay photo. I have no idea if this transfer case will flange up to your intended transmission, or will serve your purpose. See this eBay listing and make your own count/estimate, and maybe contact the seller:
Another name that pops up when you search for JF1A/JF3A transfer cases in 4X4 retrofit projects is @JowettPerformance. If you are likely to be a customer, they'll probably talk to you about what you want to do.