If your pipe, silencer, and air cleaner are all flowing well and your compression is good, your problems are very likely either carburetion or ignition.
I know it's a pain with the points/flywheel/etc., but I'd really suggest getting the ignition squared away before tackling the jetting. Your points are still available from Honda, and a flywheel puller can be found if you need one. Just for what it's worth - I replaced my MR175's points ignition with the CR125M CDI, and the bike instantly went from sluggish to snappy; I wouldn't have believed a simple ignition change could do that, but it did. Aftermarket CDI ignitions are available for your bike (they're not cheap).
Since your cylinder head takes the same 3/4" reach plugs as my MR175, I highly recommend NGK BPR7EIX spark plugs. These are projected-nose Iridium plugs, and so far they've been impossible to foul (the motor runs great too).
As far as jetting goes, it sounds to me like your original carb's pilot (slow) circuit is too rich, and maybe the needle circuit as well. There's an MR250 video on YouTube where the bike is smoking and sputtering from a similar over-rich condition, so I'd assume the stock jetting is too rich.
With the stock flywheel, your bike should idle fine if jetted/adjusted right. With my bike, I found I had to adjust the pilot air screw much leaner than I was used to, but the idle improved greatly (a leaner pilot jet will help a lot). I ended up adjusting my air screw pretty far out (2.5 - 3 turns) and then backing out the idle speed screw to brings the idle revs down. My MR175 has practically no flywheel now, and it idles OK if I run the idle a little high.
I had a similar carb on my CR125M for many years, the Keihin 36mm optional CR250M carb. Your MR250 carb is (I believe) the first power-jet Keihin. It should work great once it's dialed in, but the Mikuni should work well too.
Here's a wiring diagram for your bike. I bypassed my rectifier and the bike ran fine, but the condensor will still be needed for the points ignition.
Ray
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MR175 - MR250 Wiring Diagram.gif [ 79.41 KiB | Viewed 10253 times ]
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_________________ '74 CR125M (175cc), '75 MR175, '82 RM250Z, '08 YZ250F, '14 Zero FX electric, '14 Zero MX electric, '18 Alta MXR electric
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