> typically more like 5 or 6k.
Best load is determined by the power you want and the B+ voltage.
That assumes your tubes are "big enough". There's no huge diff 6L6 or EL34, they are comparably big.
So with the same B+, a switch from 3K to 6K tends to cut your power in half. Since you have not halved the power transformer weight, that's a poor deal.
Any tube can be run at high or low load impedance. In the past, some 6L6 users favored higher voltages (at lower current); hence 6.6K load was often seen.
But the B+ cap costs are high when you get over 450V-500V.
So both Fender and Marshall explored ~~400V supply and lowered the load impedance to suck more power. The big 5881/6L6GC Fenders run 4K per pair.
EL34 will pass a wee bit more current, at the same G2 voltage, than 6L6 types. Marshall pushed down to 3.4K. It's not a huge amount more power; also your *speaker* impedance varies more than 3.4:4 ("8 ohms" can be 6 or 10 ohms minimum, and more outside the midrange).
Leave the OT alone. Just check the bias.
Also explore 6550. Costly, but bullet-proof in EL34 duty.
Watch Pin 1. On EL34 this is usually tied to Cathode. On metal 6L6 (don't use these) and good 6550, pin 1 is the metal shell. On fix-bias amps, it makes little difference. On cathode-biased rigs, if you drop the pliers between the metal shell and the chassis you may short-out the cathode resistors and cook the tubes.