I'd do some of the following:
1. Not have TOS mentioned at all like in the rest of TNG. They didn't need a handover for goodness sake. TNG had been doing fine on its own for years. If you had to do a 'handover' I would just do some mystery that the TOS crew had left behind and perhaps Kirk giving a message to the future captain in 80 years time.
I did like the opening sequence but agree with the people who think Chekov and Scott were the wrong characters given the wrong lines.
2. Lesson the power of the Nexus to have it do time travel, endless life, 3-dimensional travel, fulfill your geatest fantasy, compel you to come back. Its too much, too incredible. Use good writing to get over script problems, don't apply more magic.
3. If you have to have Kirk have a fantasy life, have it with someone we know about with Edith or Miramanee having his brother alive so we can see that it is hurting him to go with Picard.
4. Show the natives Picard wants to save so we could care about them