It can be done, but, more than likely, it will take at least 2 hours per album. I've created needledrops, you are actually really quick if you can do a single album in 1 hour.
This is 5 Hours of paid work, you would be trading thousands of hours in your free time. Most people wouldn't work for less than $10/Hour. It's not worth your time if have to redo your efforts at a later time, for $50. Honestly spend $50 for the 2TB external drive and create FLAC files. An album at CD quality is less than a GB, so 1 TB will hold over 1000 albums.
Or if you don't need that kind of speed, there are external HDD that cost about $50 for 2TB of space. Today we have faster SSD that you can buy 1TB for about $100.
If you create a FLAC file from the needledrop, it's a fairly quick process to create MP3 files for portable devices. If you want higher fidelity, you have to redo the needledrop process. If you go through all the effort to create an MP3 file, there is no going back. MP3 is lossy and conversion back to the wave form is close, but, it's not an exact recreation some fidelity will be lost. FLAC is lossless and the wave file can be recreated exactly from the compressed file. The absolute last thing done is in this process is creating the final compressed file like MP3 or FLAC. Commonly most people remove clicks that are recorded. The wave file can be edit as you see fit. You have to create a wave file while you are recording. Creating what are commonly called needledrops is a task that is time consuming. But I am going to tell you straight out that his is big mistake. If you are only creating MP3 files, you may not need higher fidelity. There are digital plug-ins for Audicity that correct the equalization, but a signal boost is still recommended if you want higher fidelity. So you'll still need a phono stage as the one you are currently using is unusable. The phono stage is in the speakers and there is no analog output out of the speakers other than the subwoofer connection, which is likely passed though a crossover to eliminate the higher frequency signal. Something like the link I've provided will do this.
You need create an actual digital signal with an analog to digital. It's no different that one of the wall warts that you use to charge your phone.