There really just isn't THAT much to do to a Blackhawk, and some times if something's shooting well, it's good to just leave well enough alone. BUT!!! There's always something you can do to make it shoot the way you want it...
$250 isn't much to work with, most revolver-smith's bottom rung action job will run twice that. So you might need to DIY as much as you can.
And of course, there's the caveat that if you're not doing your part or if your ammo choice isn't suited for YOUR revolver's tastes, then no amount of upgrades will make it a "shoot great".
Wolff Spring Kit - Runs about $10-15. Might not be huge for you though, and you do it cheaper...
OR
Cut 2-3 coils off of the Mainspring, and pull one leg of the trigger return spring off of the stay pin under the grip panel. This will make your BH behave quite nicely, and best of all, it's FREE!!!! Even if you mess up, Ruger will often send you mainsprings for free, otherwise I think I paid $4 for a spare a couple years back.
Shim that hammer, trigger and cylinder. These are available in generic packs from spots like Midway or Brownells, or you can custom order the exact sizes you need from Triggershims.com (Lance is great to work with). If you order from the retailers, you'll get WAY more shims than you need, but you'll pay about $45 for all of it ($15 each, for 3 10 packs), whereas the custom kit from triggershims.com is $8 for 4 shims of the exact size you want. You can do this yourself and it'll help true up the travel of your action to improve the feel.
Polish the internals. A bit of elbow-grease applied wisely can really slick up a Ruger SA without ever involving a gunsmith. Won't cost you much, some buffing wheels and compound for a dremel, some super fine sandpaper (I use 400wet, 600 wet, 1000, then a leather strop rubbed with rouge), and a few hours of your life. Again, this just smoothes everything out to help improve the feel of your action.
Power Custom Free Spin Pawl, or Free-spin modified Factory Pawl: Really just makes reloading SO much more pleasurable, plus a number of other benefits. The Power Custom pawls are ~$35, modifying your existing pawl is free, or a new factory pawl is $5.
The more spendy stuff you might look at doing:
Regulating Chamber Throats: I can't say for certain that this is a 'normal problem' for the 41mags, but I know it's issue enough for 44mag and especially 45 colt. I've seen a few 357mags that had pairs of chambers, so I wouldn't be surprised if your 41mag needed a bit of a touch up on the chamber throats. If you're comfortable, Manson reamers and pilots are available at Brownells, or can often be bought used. Or there are folks on here that would be willing to do it for you, just mail them your cylinder (non-serialized part = no FFL transfers).
Ream 11 degree forcing cone: Since you're shooting cast, this will likely help you more than any other "upgrade". Brownells sells a kit, but for the cost, if you're only doing one, you can get a smith to do it cheaper.
Power Custom half-cock hammer & trigger kit: These really clean up a crisp break in Ruger SA's, and a lot of guys like the half-cock feature to make the chambers line up with the gate when open. The kits run just under $200, so this would soak up most of your budget, but for that price, you also get a Wolff Spring kit included, and it DOES give you a DROP IN fantastic trigger.
An oversized Belt Mountain basepin, locking or otherwise, might be a good investment for you. Might be purely aesthetic, or it might cure a jumping basepin for you. The oversized pins require a bit of fitting (I spin them in a drill press against fine sandpaper), but it can really tighten things up for you.
Then there are things that might not actually change the accuracy or shootability of the weapon, but could be items that specifically enhance your shooting experience with the weapon. Things like sights, grips, scope, etc...
Bowen Classic Arms Rough Country Rear sight is a great option.
A Weaver 301 scope mount and a Simmons ProHunter 2-6x32mm or Burris 2x20mm scope would fit within that budget. Just within...
Or a JP Rifles JPoint sight mount and a Burris Fastfire II (or III on sale). Should be right at $250 for this rig.
Or a new set of grips that might better fit your hand, Hogue Monogrip, Eagle or Altamont grips, etc etc etc... Usually around $50-75, higher depending on what you want.
Lots of options, but it's your revolver, and your budget, so ultimately, you have to decide what matters to you!