That's an interesting self-imposed challenge. It might be a little more satisfying with an 8-track reel to reel.
I never tried a Portastudio, but I did try a Fostex 4-track cassette recorder many decades ago. I thought they were a bit disappointing though.
I digress. Best of luck with this adventure 
I now have a Yamaha MT4X. It has better specs than the Tascam 424 and was available for cheaper.
The biggest limitation with my all-analog challenge is the drum sounds. I'm in an apartment and can't just mic up real drums, and sample-based drums (like the Oberheim DMX I normally use for more rock-oriented sounds) are by definition digital. The options I have at home are the Elektron Analog Rytm (808-ish to modern EDM drums) and the Simmons SDSV (that doof-doof sound of the Eighties with the iconic hexagonal pads).
The Quadraverb is obviously out, but I have a Eurorack synth setup based around a pair of Roland System-500 sets. The Roland System-500 consists of an oscillator, filter, amplifier, envelope/LFO, and delay, each system has a pair of oscillators/filters/amps/envelopes, and the delay is very short and intended for use as a chorus or flanger. Since I have a pair of them, this can approach the Roland Juno chorus or Dimension D. I have also added an extra case, which has input and spring reverb modules. My Moog Matriarch I normally use with the system also features an analog delay which is much longer. My FX needs are covered.
I used a Tascam (688) 8 track cassette, basically a fairly well appointed mixer with an 8 track cassette built in, I think it ran at double speed to improve the response and we used metal cassette tapes. It worked quite well (for what it was). One track got used up for SIMPTE to sync it to the Atari (running creator/noteator) which midi sequenced the keys (Korg MOne) and drum machine (Atari). So we then used the other 7 tracks for guitar, bass (sometimes) and vox. 4 Track is more challenging, albeit good practice in sub mixing. This is the era where QBase started life, running on Atari's for sequencing, they later added digital recording capability. Whereas ProTools (which came later) was for digital recording and they added the midi sequencing to that.
Funny that Cubase was a sequencer first then a recorder, and Pro Tools was the opposite. I use Cubase, but I've only used the sequencer once, when my hardware sequencers were all in the other room. I prefer to work with hardware sequencers when working with synths, I don't have to fire up the computer just to jam and save my ideas. But unfortunately, guitars can't remember musical data like sequencers and drum machines can, and digital storage is now far cheaper than tape, so Cubase is effectively my audio sketchpad.
Yes, with four tracks, I'll be in mono if I need to record a sync track. I saw the eight-track version of the MT4X, the MT8X, but the example I was looking at was untested, and the 4 has a half speed setting while the 8 doesn't - I'd like to try some tape speed tricks. Alternatively, I could record a stereo backing track (either on my Yamaha SY99 or my Eurorack synth setup) and then I'll have one live instrument and one vocal track.
Upgrading to a reel-to-reel and mixing desk will have to wait until I have a house proper.