Recharacterization due to Roth IRA overcontribution

In early 2020, I contributed $6000 to my Roth IRA. At the time, my salary was lower, so I didn’t think my 2020 AGI would go above 125k.

Then I got a new job in mid-2020, which came with a big raise. So my 2020 AGI ended up being around 134k, which means my 2020 Roth IRA contribution of $6000 was over the limit. One solution is to do a recharacterization, i.e. move $6000 from my Roth IRA to my traditional IRA. (Then later I can move that $6000 from traditional right back to Roth.)

The problem is I don’t have any cash left in my Roth; all of it is in stocks. Would one option be to transfer $6000 worth of stocks from Roth to traditional for the recharacterization? Or do I have to transfer $6000 in cash, in which case I’d have to sell some stocks first?

If I can recharacterize by transferring $6000 in stocks:

1. Can I choose any stock, or does it have to be one that I bought in 2020?
2. If I can choose any stock, how should I choose one so that I’m taxed as little as possible?

On the other hand, if I must recharacterize by transferring $6000 in cash:

1. Can I choose any stock to sell for $6000, or does it have to be one that I bought in 2020?
2. If I can choose any stock to sell, how should I choose one so that I’m taxed as little as possible?