In case anyone cares, I took the advice to sell all the alphabet soup at Ameriprise in order to avoid any confusion on the adjusted cost basis of the inheritance. It was only a small amount of gain (~1%) due to most of it being in bond funds (and with the adjusted cost basis very little time to appreciate) so the tax hit was acceptable.
After comparing costs at Ameriprise and at Vanguard I found that Vanguard would only be a bit cheaper because a lot of the alphabet soup was in ETFs which were free at both places. I begrudgingly paid the steep per-transaction prices at Ameriprise for the peace of mind about cost basis.
Anyway, I guess I ended up not actually "transferring" the account as I liquidated it and just moved the cash to my regular investment account, hah. I did have an inherited IRA that I transferred in kind though as there was, obviously, no concern with cost basis being a traditional IRA.