very low powered tweed

[m-fine]

Both of Scott's suggestions are good.
Another idea is to have seperate 560R cathode resistors for each 6V6. Switchable dual pole bypassing with 100 or 220uF caps (needs to be bigger than stock as not getting the benefit of signal cancellation from linking the cathodes). Unbypassed ~ halves the clean output power (and reduces the gain a little). Though the overdriven tone isn't quite as compressed as when cathodes are bypassed. Bypassed the tone and performance is as per stock.

That is what I would try. Here is a thread on the topic with a few different approaches and some diagrams to help you out. You can do it with switches or a pot which is pretty cool. I have not tried this myself yet, but I definitely plan to.

Disconnecting one output tube in a push pull amp