There are many things to consider here. First, don't worry -- you're not straining anything other than possibly your voice coils if in fact you were clipping your amp. I don't think that's the case. More likely, your passive controller is the first problem. The input sensitivity of the Anthem tube amp may be (I couldn't find the figure on the web) too low for your sources to drive it to full power. An active preamp or at least a TVC (transformer volume control with +6db of passive gain) is probably called for. By your description, I take it you're running your volume control wide open and still not getting what you want, which gives you the impression you're "straining" your system.
It would be helpful to know more about your room, with respect to size and furnishing characteristics to guess your perception of the dynamic range of your system. You certainly could use more power but may in fact not need it if you have some voltage gain in the preamp stage. You can figure your 40/40 watts of RMS power from the tube amp have a good 3db of headroom on bursts. Also, does your amp have 4ohm output taps from the transformers?
There are a lot of ways to get more power if you like your speakers, but many of them won't please you if you're accustomed to the qualitative aspects of your amp. You can try a pair of the excellent Channel Islands D100 or D200 monoblocks on home trial with return privileges, and that is a quite musical and affordable solid state option. Another thing is to consider much more efficient speakers, Such as Zu Druids (101 db/w/m) or something Omega, for example. You might be surprised how much better things sound when your power amp isn't squeezing sound through a speaker crossover.
Phil