WARNING: Tube/Valve amplifiers use potentially LETHAL HIGH VOLTAGES.
Building, troubleshooting and testing of these amplifiers should only be
performed by someone who is thoroughly familiar with
the safety precautions around high voltages.
In 6L6`s there were low power types 6L6 metal or 6L6G (ST glass bottle) that only have a plate dissipation power of around 19 watts. Then there was a high powered version called 6L6GC, common in guitar amp applications good for about 30 watts dissipation. If you are planning to use 6L6GC`s you ought not run any risks.
Depending on how your amp is wired to bias the output tubes you may be OK (self bias) or can adjust the amp to use the lower power 6L6 types (adjustable fixed bias). I suspect your RCA`s may be the low power type if they have the ST shoulder style glass envelope.
I think you mentioned that your amp came with 6P3P`s. In that case plug in your 6L6`s and keep a close eye on them in a darkened room. If the plate (the outermost mettalic structure inside the envelope) shows any dull glowing red or orange areas shut down immediately and do not use these tubes without further consultation. When I say glow, I am not referring to the normal filament glow in the center which all these tubes have.