Thanks for all the valuable info.
After studying specs and reviewing your comments, I'm leaning heavily toward the Keysight 34461A because:
1) 34661A's immediately available from the factory (Don't want to buy through distribution/dealers) unless I'm missing something here. 2 day delivery. I hate to wait! DMM6500 quoted 33 weeks!
2) The specs for the functions I use most are adequate to very good (Low Frequency AC, DC Voltage, Resistance, Diode, Continuity, Capacitance).
3) I like the tighter specs on the DMM6500 and the Lo-OHMS range but I don't like touch screen interface on anything.
4) The 34465A is nicer but I can't justify the extra $400 for what I intend to use it for.
The only spec I don't like is the AC-coupled TRMS. I like a switchable choice, AC or AC+DC.
I'll keep studying and I'll keep an open mind to any additional comments.
Thanks so much for all your input so far, especially on the promo program.