On this forum we are really rarely recommend to use any type of pass and your case is not an exception. We wouldn't recommend to use pass for your travels. Your second option would be much cheaper and actually not that difficult to accomplish:
For Paris-Stuttgart leg you can purchase discounted ticket. If you buy in advance, then tickets start from 29 euro (can be bough on either French railways website - tgv-europe.com or German railway website -
http://reiseauskunft.bahn.de/bin/query.exe/en?newrequest=yes&protocol=http:& , so just check which one offers better fare for your date).
Lander ticket is perfect solution for a group like yours, so your choice couldn't be better, but just as a small note - if you don't plan major railing on Day 4 you might not need Lander ticket, but City Pass for instance, just count whether it worth its value for your Day 4 plans.
No problem with luggage on Black Forest scenic ride, between Offenburg and Singen there are standard DB regional trains, so plenty of space there.
For your Swiss plans we kind of have doubts about involvement of Eurail again, especially since there are other cheaper options. For instance, SuperSaver tickets (
https://www.sbb.ch/mct/wi/shop/b2c/adw.do?4004) for route Basel-Luzern cost from 12.4 CHF, for Luzern-Interlaken from 12 CHF, Interlaken-Zweisimmen from 11.6 CHF etc. The only negative thing is that officially last day of use of SuperSaver ticket is March 6th, but it might be prolonged. If not, then you can at least use SuperSaver tickets for the first part of your Swiss trip, afterward just purchase full fare ticket and it would still be cheaper than Eurail tour.
Basel-Paris tickets start from 20 euro on French railways website, but again you need to purchase those in advance.