Sounds like you are already doing it the best way. Why bother with 'specialized' hardware. The only way that might be better is if the adc/dacs were better in the external hardware. As long as you have a decent soundcard, everything will work out fine. Just make sure you are plugged into line-in, not mic-in, and set the recording level appropriately - somewhere around -3db will leave room for unexpected peaks without clipping. You can always normalize it closer to 0dB if you want it as hot as possible (or compress to make it insanely hot like modern cds).
The only thing I would suggest is to use a good audio editor, like Sound Forge, to do the recording. That way you can then edit the files, make tracks, remove hiss, compress, normalize, etc to get them the way you like.
I've yet to record from an LP but I do it all the time for cassettes. I record the entire side of one cassette as a wave file, then edit it and split into tracks, then burn.