joining the traffic pattern quandary

So if a RIGHT turn is permitted by the FARs onto downwind, then so
must a RIGHT turn onto final (where left traffic in effect).Hence the
quandary

There is no quandary.

The 45 right-turn entry into downwind is recommended by the AIM and
would not be so if it had ever been held to be illegal.

Once in the pattern, left turns are mandatory unless the stated ground
signals exist, if it's an untowered airport.

What's so hard about this?

then I could do a 90 degree right turn onto short final,
where left pattern is in effect.

No, you couldn't. Pilots have been violated for this and it has been
upheld by the NTSB. You would have to intercept final at a
"considerable" distance from the runway in order to not be "in the
pattern." The distance depends on what type of airplane you're
flying.