You have the most anemic version of the 5M that came out, good for 150 peak hp. The 85 5M had 172 hp due to higher compression, intake manifold, electronic ignition, a potentiometer-style TPS, a knock sensor and a much better ECU system that could fine tune the fuel/ignition curves. Adding a header and bigger exhaust helps the power out a bit, too. I think the 3.73 gears are just too high for that weak of an engine, and would be better suited to a later model or modded engine. The turbo guys LOVE those 3.73s and the rare 3.42s to help build boost quicker, so you have gearsets that you could always sell.
My first supra was an 83 p-type with an automatic. It was a feb. build date so it had the 3.73 gears in it. It was very slow on takeoff and I had to downshift to pass or climb hills, but it got decent gas mileage. I soon added a Pacesetter header and catback exhaust which helped it out a little. It never did have low end grunt though.
Do you want more power, lower gears, or maybe a little of both? No one has mentioned the 3.90 gears that come in the Cressida sedans from 85 to 88. They usually have open diffs, but you could swap in the lsd center section along with the stub shafts from an lsd diff. Yes, there IS a difference in the little stubshafts between LSD vs. open, so keep the stubs with their corresponding center section. It's also good to keep the r&p with it's case, to make shimming the pinion depth easier.
You can bolt on a few parts to make more power, but you can also tune what you have. I'm sure you already know about advancing ignition timing. On our engines, the cams can be advanced/retarded individually in relation to TDC, and you can also change valve overlap. Toyota uses a dowel and a series of holes in each cam and cam gear to allow for machining varience, but racers back in the day used them to fine tune the cams and move the powerband. 82's even got 5 holes in each cam instead of the later cams only having 3. There are threads on the forum or in archives all about this.
The main reason for noise from the rear end is the pinion bearings losing their preload because the crush sleeve crushes more from pinion deflection. Weir makes a solid spacer and shims for us to eliminate that weak link. They also make an lsd gripper kit that replaces the weak parts in the lsd that break or wear and reduce the locked effect. You could also shim the springs tighter, and research the right kind of oil to use in the rear diff to make it perform correctly.
*Horsepower figures quoted from engine specs that I looked up in a Motors repair manual in a public library back in 2002.