I have got Raspberry Pi Zero W which, I believe, is comparable to RPi1 B+. I can have Ardour working on it, even with 8 channel USB soundcard. Once you get it working you will discover that very little functionality of Ardour will be available to you, 3-4 tracks with EQ, maybe compressor on each at best. You should try another, leaner DAW - Qtractor - which is available from Raspbian repositories.
As for your problem: Try using JACK backend instead. Install Qjackctl and try to start JACK engine with TASCAM soundcard. I too have problems when I use 8 channel soundcard with ALSA backend : Ardour sends I/O error and complains about not being able to recognize channel count. When I connect my card via JACK, Ardour works just fine - and the situation is the same no matter if i use the card with RPi, laptop (Debian 9) or desktop (Debian 9).
If you use RPi1, full Raspbian may be too bloated system. I use raspbian-lite with only xorg, alsa, fluxbox wm and apps used for audio production, nothing else. Also make sure that you use SD card of sufficient read/write speed (U3, U6).