don't give up on the bullseye, I have worked up 170gr loads using bullseye with mag primers, I only buy mag primers for all pistol reloading so I cannot help with that part of your question. but I have started with the SIERRA 170gr FMJ and tried bullseye, titegroup and WST. The titegroup was the clear winner, but the bullseye was consistent and nowhere near as dirty as people complain it is. I started my loads at 5.0 since I had almost no real data to go off of, ran them up to 5.8, none showing any pressure sign, and all were moderately accurate with a chrono'd speed of 980 on the low side(too low) and up to low 1100's on the high loads, I could have gone farther but I didn't feel the need when less titegroup finished out the day with better accuracy, slightly higher speeds with almost identical powder charges. I ran the TG with published data from 5.2-5.8gr ending up with lows in the 1000 area give or take 20fps and the higher loads giving impressive 1200's from the extra long lever-action with a 20" barrel. But no brass gave me any issues with pressure signs or "dirtiness" and although the TG runs at slightly less pressures with better outcomes, no reason the Bullseye couldn't be tweaked to be a safe load running decent numbers from even a revolver. I think you just need to pick a low and safe start point, find a published max to stay clear of, and i'll bet you can make a decent load....as for the primers, your just gonna have to try and maybe seat a little deeper with a little more crimp than you would usually use. there are internet loads that give very little info, and although the velocities are rarely matching or even close, I do find their starting loads to be reasonably within safe levels, but I still drop 10-15% to start since the authors are unknown.
I think TG is your closest match for load data, but obviously you need to drop a good bit starting out, other good choices would be WST, Universal and of course HP38. I believe except for density, load data and velocities are very close matches between TiteGroup and Bullseye. Have fun, here is a site that may help get you started for odd combinations.....as for the primers? can you really not find mag primers? I would save the pistol primers for lighter bullets and high density powders where you not playing too close to the pressure territories of a half full case of fluffy stuff.
use this site with caution and if you have data to match it up with or better yet a quikload or a close to weight/profile that's published, triple check and reduce when using this site as a guide.
http://www.handloads.com/loaddata/default.asp?Caliber=357 Magnum&Weight=All&type=Handgun