Ok, so the two most obvious 'substitutions' for the expensive rail pass are either using discounted tickets or a bit slower regional trains. Smart combination of both can do wonders with itinerary like yours, but there are still certain obstacles involved. Like with discounted tickets it is need to buy them in advance, sometimes a few month in advance (only that will guarantee a good price), also discounted tickets are 'tied' to a specific date and train, so it doesn't really allow a lot of flexibility. While regional train which cost less might be slower comparing to high-speed, although sometimes regional train is the only option, so then it doesn't matter.
But anyway, let's take a look at each of your legs and see what can be done:
Paris-Zurich: for August 1 there are still many discounted tickets available for almost any direct train, as of now they start from 45 euro (which is an more or less ok fare for this connection). Such discounted tickets can be bought from tgv-europe.com website. Alternatively you can even fly relatively cheap, for instance Vueling have a good fare for August 1. So if you acting now can get you a reasonable price.
Zurich-Italy: well, Bernina Express is a tourist train, so you can't really expect any cheap price here, but at the same time nobody forbids you to take a regular local trains, which run on the same route to Tirano. You won't loose in scenery, but can pay much less, since SBB (Swiss Railways) offer special
SuperSaver tickets that can save you quite a lot. The only thing you will need to do is to buy your SuperSaver ticket 2 weeks before the travel date.
Northern Italy and down to Florence: here since all the segments are relatively short it makes sense just to rely on regional trains and purchase your tickets already in Italy, even right before departure, it will give you flexibility and be a cheap solution. All the fares can be checked via
TrenItalia website, but for example regional train ticket Turin-Genoa cost only 11 euro, Genoa-La Spezia 7,3 euro, La Spezia-Florence 11,3 euro etc.
Florence-Rome: here you have two options, either again use regional train and don't worry about prepurchsing ticket, since you'll just buy it before departure for 17,3 euro or buy in advance discounted 'MINI' offer ticket for high-speed train (start from 9 euro)
Rome-Munich: again more or less two options. First will be to fly with low-cost RyanAir from Rome to Memmingen (Memmingen airport is a bit fare from Munich, but at the same time Rome-Memmingen tickets are cheap, so it will be worth spending some extra time on route Memmingen-Munich). Other option is to buy in advance discounted ticket for the overnight CNL train Rome-Munich or daytime from Verona to Munich (with additional domestic ticket Rome-Verona)
Munich-Cologne: again you can choose between flying or going by rail. GermanWings have a nice fare for the flights Munich-Cologne, while while
German Railways (DB) offer discounted tickets for high-speed trains
Cologne-Brussels: here you more or less have only purchase in advance (via DB website) of the discounted ticket (start from 19 euro) for high-speed
Thalys trains
Brussels-Amsterdam: though even full fare tickets aren't that expensive, but still
purchasing in advance can give you a better fare
Amsterdam-Paris: also buying in advance via tgv-europe website or
Dutch Railways is the most affordable rail option. Also here (as well as Brussels-Amsterdam and Cologne-Brussels) you can check out bus options
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