Here's what I have found on the web. Update January 2, 2021
Strict 6V6 equivalents should be OK:
5871 - made for mobile (high vibration) operation, no interface resistance means high-purity cathode
7408 - specifically for audio; "controlled zero-bias characteristic"
Different heater currents up to 0.75 amps should be OK with AC heating, but the dropping resistors must be changed, and when the DC heater upgrade is available, it will not tolerate more than 0.45 amps:
6K6 - 0.4A heater so may need slight change in dropping resistors
5992 - Red Bank super reliable but 0.6 amps. Data sheet curves look less linear than regular 6V6's.
EL84 might work, with a 9-pin adapter if there is one, plus a change in bias resistor. I have not looked into it yet. High heater current, AC heating only
6L6 and EL34 need too much heater current even if AC heated
9-pin (needs adapter) There are five but they ALL have different pinouts!
6CM6 is an exact equivalent - 9CK socket
6BW6 is an exact equivalent - 9AM socket (pin 1 internal connection, pin 6 N/C)
6061 is an exact equivalent - 9AM socket (pin 1 N/C, pin 6 internal connection) - rugged/reliable
6973 is an updated version, with slightly different specs - 9EU socket (n.b. identical to 6CZ5 but specified for audio)
6CZ5 is an updated version, with slightly different specs - 9HN socket (n.b. identical to 6973 but specified for TV vertical output)
7-pin (needs adapter):
6AQ5 - same as 6V6 but 250v max (OK for Moreplay)
6005 - GE 5-star industrial rugged, reliable
6095 - same as 6AQ5
6669 - for car radios; tolerates varying heater voltage better
6928 - Very rare, very expensive; rugged, reliable, long-life, more linear than others