OK, got it sorted out, and taught that since I got some brilliant ideas from here, I should share experience for any future possibly interested traveller.
First of all, the journey southwards.
Prices for the Bernina express purchased in Switzerland are expensive. But there is a trick to obtain a much better price by purchasing a trip that starts from Germany, in order to take advantage of the Europe supersaver prices offered by DB. Mark Smith on seat61.com has all the gory details. So I got tickets from Singen (in Germany, not far from the swiss border) to Tirano, for about 50% of the price asked from within Switzerland. Of course, the first two legs of the journey, from Singen to Zurich to Chur, will not be used. Those tickets cannot be printed at home, I will get them in the mail. Total price for 2 people, mailing charge included : € 57,70, instead of 63 per person if purchased in Switzerland. Not bad... From Tirano to Milano, I also purchased in advance because the transfer time is only 20 minutes, and there might be a queue at the ticket machine. From the trenitalia web site, € 11.50 for two tickets from Tirano to Milano Centrale.
Journey northwards, complicated because no site seems to be able to sell the whole journey, for the trains that I wanted to use, via the Gotthard summit line. So, found the right train (if it stops at Airolo, it means it doesn't go through the base tunnel) from the DB web site, then purchased tickets from Milano to Chiasso on this train from the trenitalia web site (€ 11 for two) and then proceeded to purchase Chiasso to Zurich. A bit surprised by the price (not the same as in Italy, we're in Switzerland, after all!), I taught I could use the same trick as for the previous day. So, went back to bahn.de, asked for a Chiasso to Singen via Erstfeld and Zurich connection, and got again a Europe Supersaver for € 40 per person instead of the € 60 asked by sbb.ch. This time I got print at home tickets.
Result, 160 € for a wonderful double crossing of the alps, for two people. Not bad. Thank you, Mark, and also Lemonic for his suggestion to split the ticket.
Just a final warning : the sbb.ch website is trying to cheat by first suggesting prices that are available only if a price reduction scheme applies. Only when it comes to listing the traveller names, you get the option to specify whether a reduction scheme applies for you. And if you tick the "no reduction" box, the the displayed price doubles... A bit unfair in my opinion, a bit like the airlines sites that add all taxes and fees to the price just at the last moment before committing to pay.