The post service won't expect a stamp if you are sending something to an “Antwoordnummer”. They can tell and decide who to charge based on the address itself. It doesn't matter if it's a loose reply card, an envelope with the address printed on it or something you prepared yourself.
From the handy iAmsterdam site
Amsterdam Centre District refuse collection
Either take bulky refuse to a waste collection point (in Dutch) or telephone 020 256 3555 to register it for free collection. There is no scheduled bulky waste collection in the Centre. Once you have arranged collection, put items on the pavement on the ...
Carry it up to your apartment - that would be simplest and safest.
I ... don't really want to drag it up 3 flights of Dutch stairs to my apartment
Hauling a bike upstairs is indeed a harrowing experience, and I wouldn't recommend it for a few days away, but given that you're leaving for several weeks - it's worth it.
Like @EugenMartynov suggests - try ...
Update as things progress:
In late September, WaterNet sent me a letter, informing me my annual service charge was being reduced by 55.08 EUR. So, apparently they got informed at some point about my de-registration. However - the total charge had been 269.56 EUR, and I left after 169 of 364 days of the year, so that din't make sense. I've written them to ...