Saving money on Rome to Munich train travel w/ multiple stops inbetween

Not really. Sounds like you are asking for some sort of open ticket which allows stops en route, these do not really exist on trains.

Except, between Garmisch-Partenkirchen and Munich, you could get a "Bayern Ticket". This is a one-day pass for the whole of Bavaria, not valid on IC or ICE trains (you would have to travel on stopping trains from Garmisch-Partenkirchen to Munich), but it includes all Urban transport in Munich (S-Bahn, U-Bahn, tzrams and buses). It's big adavantage is huge discounts for more than one traveller:
1 passenger: 23 euros
2 passengers: 28 euros
3 passengers: 33 euros
4 passengers: 38 euros
It is also not valid before 09:00 Mondays to Fridays, no limit at weekends. Details are here: http://www.bahn.de/p_en/view/offers/national/regional/laender-tickets/bavaria-ticket.shtml

Actually this type of ticket used to exist and may still exist but you will probably need a travel agent specializing in trains to pull this off and it may have lots of other restrictions.

My only experience with this type of travel was probably 10 years ago traveling from Zagreb to Salzburg with a stop in Ljubljana along the way. I found a travel agent (via the tourist office) in Zagreb who sold me something called a 'star' or 'starpreis' ticket that was booked Zag to Salzburg. She then sold me separate reservations for the two different trains for the 2 legs of the journey.

Additionally, the ticket was sold as a round trip since it cost full price for the first adult, half price for the 2nd adult, and I believe a quarter price for each kid. The overall price for the round trip (with the return portion thrown away) was less than buying the one way ticket.

I'm assuming a lot has changed since I took that trip and not sure if these types of tickets still exist. I have not come across others mentioning these types of tickets but then again it took a local train specialist to bring this to my attention.

I would expect an "open" international ticket to apply only to trains that don't require reservations, therefore not the Le Frecce trains in Italy, although you might be able to use it on an InterCity and pay a seat reservation fee. But you'd also be paying base/full rate, with perhaps some savings based on distance, but not getting any of the advance discounts associated with reserving ahead. So I would not pursue that idea for this trip.

Just buy tickets to your particular destinations whenever you are ready to commit. If you have hotels reserved, then you probably are ready to lock in at least to your longest trip, Florence-Innsbruck, and can get some savings on that route.

You're not traveling far enough to get good value from a rail pass, especially since you're not even entering all 4 countries that you would pay for.

"I looked at Eurail, but the 'Select Pass' country option is more per traveler than the total for all of booking the individual legs."

That's usually the case these days. Good for you for doing the homework before buying anything; some people buy the pass first, assuming it will be cheaper and easier, and then run into problems.

If you don't want to tie yourself to a cheap booking made well ahead then buying 'walk up' tickets on the day for regional trains (often in multiple hops) may be your only bet if you are watching the $$$. The longer journey Florence to Innsbruck you may like to book ahead.

For Garmisch-Partenkirchen to Munich, instead of a Bayern-Ticket (33€ for three persons), you can get a Regio-Ticket Werdenfels for 27€. Here is the Bahn page about it (it's in German). It's like the Bayern-Ticket except for a smaller area. There is also a link on that page to a map of the covered rail lines. It's valid for unlimited regional trains on the main line from Mittenwald to Munich via Garmisch-Partenkirchen and Tutzing, in the Munich metro district (MVV), on the Außerfernbahn as far as Pfronten, and on spur lines to Oberammergau and Kochel as well as RVO buses in the area. Same time limits as the Bayern-Ticket.

Three Austrian Rail tickets from Innsbruck to Garmisch-Partenkirchen are 14,40€ each, or 43,20€ for all three. So, with the 27€ Werdenfels ticket, Innsbruck to Munich with a stopover in Garmisch-Partenkirchen will cost 70€.

An open ticket from Innsbruck to Munich from the Bahn would allow you to stopover in Garmisch-Partenkirchen for more than a day and continue on using the same ticket, but it would cost about 100€ for the three of you, so using the Werdenfels ticket would be your best option.

Thanks to all for the great replies! It sounds like passes will not be the way to go (other than possibly the Bayern-Ticket).

We did basically the same trip you are doing and we booked point to point tickets for each leg. I printed them at home and had no problems whatsoever. It was cheaper than any pass I found. I did not find my way inconvenient so I can't comment on whether or not passes are inconvenient. Hint for you to remember on your journey: make sure you read your tickets in Italy to know whether you need to have your passes validated. Italy was the hardest to travel in via train because of the validation factor. We left Rome and didn't validate our ticket and got fined on the train 10 euros. We had a paid ticket but failed to validate it. Still don't know how to validate a ticket in Italy or why some tickets need to be validated and others don't. Didn't ruin our trip, though, it was a learning experience.

Jenny