Just got back from Amsterdam post-change to the Museumkaart policy.
Here is what worked (if you're in town long enough - but also see below for a hack)
1) Buy the Museumkaart at a participating museum right when you get to town. This gives you 5 visits for your 60E in any case - which you'll break even on with 4 visits to top museums, all of which are 15E and above.
2) Right then and there, fill out the Dutch form to register your Kaart based on its ID. https://www.museumkaart.nl/registreren. Use Google Chrome with Google Translate (even on your smartphone or tablet) and it won't be a problem. You don't have to pay anything so not having a Dutch bank account (as the EU version of the page assumes) is not a problem. See more detailed comments below.
3) Visit nice museums with your temporary card while you wait. The Dutch mail delivers 86% of letters within 24h, so it's really down to how fast the Museumkaart folks turn around. I registered on a Tue night and got the unlimited card on Friday, meaning in all likelihood, they processed it Wed and put it in the mail Thur.
4) Now you have an unlimited Kaart, good for one year
Use the address of your hotel (let the front desk know) or your AirBnB (put a sticker with your name on the mailbox and get the key from your host). If the mail carrier bounces the card back, you lose.
In the address form, there is no place for the street - the Netherlands have this postal code overlay with 4 digits+2 letters that goes down to street level. Your house# goes into the second box. Your floor/apartment number goes in the 3rd box. For AirBnB situations I highly recommend the sticker on the mailbox to make sure the mail carrier actually drop.
You need a picture of yourself for the form. Just take a picture of your passport image with your phone and submit that.
Speed hack: IF you can talk someone in Amsterdam (e.g. your AirBnB host) into getting a temp card for you and send you the number you need for registering it, you can cut the wait time to zero and have a registered card on day one
Tip on the EU version (https://www.museumkaart.nl/Registration): Maybe you're spending time in elsewhere in Europe and can pick up the card at that address to cut the lead time to zero. But you don't have a bank account with an IBAN and a BIC to pay the admin fee of 3.25E. In that case, consider using TransferWise (I'm not getting paid by them nor do I guarantee anything about that service BUT it's worked for me). They offer a socalled borderless account that comes with an IBAN and a BIC and you can deposit a few euros from your non-EU credit card in the account in under 5 minutes.
Hope this helps.