Doubling the power will buy you 3dB more headroom but there are other benefits to a separate amp over a receiver is some cases. When driving a low impedance, highly reactive speaker load, a separate amp will usually have lower output impedance since it has more output devices, thus suffer less ill effects of frequency response varation under reactive loading, lower distortion and a higher damping factor for better woofer control.
I would suggest trying what you have now, crossing over your main speakers at 60-80Hz and letting the sub handle bass below that. If you are not satisfied, first consider speaker position and room acoustics before dumping more money on electronics. A good 2Ch amp can be had for around $1k or so, but first get the basics right before upgrading again.
PS. While swimming you should be thinking of ways to make money NOT spend it