Not sure if this helps but there may be an option from Rome to Munich using Freccia argento and Eurocity service. and then Munich to Ams via Frankfurt is predominantly on DB ICE trains with no reservations needed.
With all the problems with Thalys going via Nice/Paris is a no no.
A quick check shows services from Rome to Munich tomorrow morning at 6.50/1610 or 0910/1827, and then Mun to AMS on Sunday at 7.28/1529 via Frankfurt airport with no reservations. There are several later options on both routes.
Just need to ask at Rome termini for reservations but OBB suggest seats are available.
Your route should be possible, the nighttrain Zütich-Amsterdam has optional reservation for seats (but the train is often full, so book a reservation via bahn.com or oebb.at (seat only option). For Rome-Milan and Milan-Zürich schuold be possible via ÖBB online with the one way ticket option and as discount Interrail/Eurail Global Pass. You have to search Rome-Milan (10€) and in a second moment Milan-Zürich (11€). If it doesn't work for Milan-Zürich, you can use reservation free local express train RE to Lugano and change there or in Chiasso to the first train to Zürich. In Switzerland trains have only optional reservation (also the train from Milan).
There appears to be not a single ticket on any train from Milan to Zurich - can this be right?
For future travellers:
Pass holder seats in the EC trains from Milan to Switzerland are quota-controlled (€11). However, a reservation is only required until Chiasso or Domodossola and pass holder seats from Milan to those stations are not quota-controlled (€10). So unless these trains are completely full, it should be possible to book a pass holder seat between Milan and Chiasso or Domodossola.
. Thank you