I've been racing vehicles with one-piece rear axles (Formula 500 and Shifter Karts) for the better part of a decade now. Turn-in understeer will always be a challenge, and anything you do to fix it will tend to lead to corner-exit oversteer. However, it's not all doom and gloom. F500 is probably your best analog, since the cars are similar sizes (55" width, 80" wheelbase, 10x8" wheels), but we do carry considerably more weight (800# with driver), and have slightly more power (~135hp). None the less, F500 autocross speeds tend to be pretty close, albeit slightly behind, FSAE cars. According to the SCCA PAX system, F500 should be about 95% the speed of FSAE, and shifter karts (KZ2 spec) about 97%.
One of the biggest tricks that many people overlook is front end caster. We use a TON of it. Pretty much the more the merrier, as long as your driver can still turn the steering wheel. This is done to promote weight jacking - in the shifter kart I have enough of this that when the car is at full steering lock, the inside rear tire will be 2" off the ground while sitting still. With a soft suspension the effect will be minimized, but still remember you don't need to actually get the rear tire airborne, just reduce the weight on it so it can slide.
Since you'll have an independent rear suspension, another trick you can do is to run a massive rear sway bar. Combine this with a lot of body roll in the front, and you'll be lifting the rear tire in no time. However, one of your biggest benefits to a spool will be reduced weight - you may find that you'll be able to drop the weight even further by having your rear axle serve double-duty as your sway bar as well. We effectively do this (albeit as a requirement of the rules) in F500 by running a 50mm kart axle suspended by two rear uprights connected via a 4-link + watts link setup.