"I know Eurail doesn't cover Berlin > Prague and Prague > Mainz"
Eurail does cover Berlin > Czech border and Czech Border > Mainz. However, that first leg might be done more cheaply by regular ticket than by using a railpass day - reg tix cost about 40 euros. Passage within the CZ republic should be pretty cheap.
Mainz-Bacharach: use the Regional trains for this route and it should cost less 10 Euros or so.
Reutte-Mittenwald: 11 Euros on a beautiful route. No railpass day needed.
Mittenwald > Salzburg: Save a railday here. Go via Munich on a "Bayern Ticket" single (19 Euros) or group (2-5 people, 27 Euros total.) You must travel after 9 am weekdays (but anytime is okay on Sat or Sun) on the regional (RE, RB, IRE) trains. Buy this ticket from a DB ticket machine for the cheap price - costs more at a counter.
Salzburg > Hallstatt: Couldn't be worth a railpass day! Cost is about 5 Euros.
So... I sorted through some of the shorter routes on the national railway sites to obtain ballpark prices. Possible routes for the Eurailpass days. Looks like 8-10 days will work for you:
AMS - BER
CZ border - Mainz
Bacharach - Interl.
Interl. - Gimmelwald (Gimmelwald is tough to get to. about 4 Euros to Lauterbrunnen; beyond that, you'll have to check private railway costs. I'm not sure what discounts a Eurailpass may give you on these or if they require a railpass day. Personally, I'd look at staying in lovely Lauterbrunnen and spending any extra cash on a trip to the Schilthorn - magnificent.)
Gimmelwald - Reutte
Hallstatt > Vienna (about 45 Euros reg. price)
Vienna > Venice
Venice > Rome
Rome > Vernazza (only about 30 Euros)
Vernazza > Paris
Hope this helps.