I don't have tubes or audio transformers yet + a couple of components that just arrived today, so I'm not quite ready to measure yet.
Heating elements in general can be tough - and I think the same holds true to tube heating elements. They usually have a low resistance, so it can be hard to tell vs a short to ground - which is why they have a significantly higher current rating.
I'm still learning about this as I go as well, and you're a little further along than I am, so I'm looking forward a bit, but when I get to the point of applying power, (just thinking out loud) I would expect that if the transformer is rated for 6A, I would expect both boards to draw 3A max - hopefully closer to 2A for working headroom. In that case, if you measured a minimum of 3 ohms per board, you should be ok for the transformer. This is really close to continuity on a lot of meters, so if you're just checking for continuity to ground, it might give a false positive.