I think you'd find a lot of support for this issue. I know there have been 2nd gen Odysseys before (not sure about 1st?), but don't recall seeing a Sienna. I do know that an Isuzu Oasis was on the 'Want to see in Lemons' list, at least awhile back.
I'm partial to GM stuff, so I'd probably look at the U-body vans.
There are some 1st gen vans racing (OnkelUdo has lots of experience) -
- Judges seem to love them
- Base models used a Chevy 60degree V6, which has lots of upgrade options, but most came with the Buick 3800 V6, which is pretty solid itself, but could probably be swapped out for the supercharged L67 for 240hp/280tq, only problem would be space (but isn't that what the plasma cutter is for?) There's also a budget-friendly path to a manual transmission here as well.
Second gen van could be good, I've seen a picture of one, but don't know too terribly much about them. To my knowledge, these all came with the 3400 Chevy 60degree V6, which makes good power, but won't do it for long on the stock plastic lower intake manifold. But, a better quality, metal LIM is $100 and an afternoon (maybe a day) away. These come with a slightly beefier 4T65E transmission, compared to the not great 4T60E in the gen 1. Not sure about manual swapability, but, probably similarly easy to gen 1. *Bonus - this is the gen that the Pontiac Aztek & Buick Rendezvous got built off of. I've frequently seen the Buicks (and, honestly, the rest of them) going for Lemons money with 'incurable overheating issues' (i.e. a bad LIM and, possibly, head gasket) - so, that frequently means new water pump, radiator, thermostat, ignition parts, etc, all thrown in for free! I believe the Rendezvous is on the 'Want to see in Lemons' list, because, for some reason, one still hasn't turned up. They were also later available with GMs stout 3.6L DOHC, but, probably harder to find that in budget.
Third gen van, or, what I'd probably go with. Remember when GM decided they wanted their vans to look like 'Sporty' SUVs? Yeah, these are those. Not pretty, but, I'd have to imagine that protruding nose makes working on it vastly more straightforward than the typical van with a 1' deep window into the engine. Engine options are the 3500 (LX9) and 3900 (LZ9), the final iteration of the 60degree V6, mostly the same as the Impala and lots of other GM cars. 200hp/220tq and 240hp/240tq, respectively (and the 60degree engines all tend to be very, very torquey). Better 4T65E transmission, but, not sure if the budget-friendly manual option would work in these. The 6-speed from a G6 GTP should bolt right up, and should be pretty straightforward if you get the PCM. Not cheap, because GM sadly sold very few of them, but, they exist. *Edit: These were also available with AWD, albeit only with the 3.5. Rendezvous could (and largely did) have AWD too. And, as if in a sign from the universe, a fleet-only shorty Uplander passed by me when I went to the store after posting.
Suspension upgrades do exist (at least for gen 1s, not sure about the other two), and really great brakes are a small amount of work away. It sounds like you plan to go Japanese, but, thought I'd give you some options anyways! I'm sure a second-gen Odyssey with a 6-speed swap would be tons of fun - who knows, maybe you could even keep the terrible automatic alive for a whole race!
Semi-Sentient Centenarians
1996 Buick Century - we upgraded our crappy GM sedan with parts from a crappy GM minivan.
"It's got a van motor, a 220 cubic inch plant, it's got van tires, van suspension, van shocks. It's a model with the catalytic converters ripped out so
it'll run good on regular gas. What do you say, is it a racecar or what?" - Blues Brothers, Probably