Sounds like you're recording just below clipping. Try giving yourself a bit more headroom and just don't record as hot. It doesn't need to be just below clipping. I'd say it shouldn't be but I don't want to get into an argument with some total ass who thinks everything should be as loud as possible because the manual for their software told them so. So let's just say you could stand to go in at about an average (not peak) of -18dbFS. Just try not to peak above -10 to -6.
I know this doesn't solve the thwumpies issue you're getting per se, but it's worth consideration in general.
I was going to suggest putting your amp on a chair to reduce floor reflections but then I realised you're recording line-out. I'd recommend modelling or using a mic over that, but having spent a lot of time going direct line out because I had no other option, I understand the issues.