Can a participant choose to have his required minimum distribution calculated using his spouse for the J&S calc if someone other than his spouse is his beneficiary? In other words, can they be different people?

When calculating the RMD on a joint life basis you must use the named beneficiary with the shortest life expectancy (assuming multiple beneficiaries) and then also compare this result to the MDIB result (use the shorter of the two results) since you would be using a non-spouse beneficiary. If a trust is named as beneficiary and the spouse is the beneficiary of the trust, I believe you could use the spouse in the calculation, but you must make sure that the trust satisfies the rules in order to be considered a valid beneficiary designation for purposes of the RMD rules.