Amsterdam annual number of visitors picked up the pace and is now more than 30% higher than it was in 2010. Business-side demand increased substantially, and the expense-account travelers are the first to crowd out accommodations, with a knock-down effect (people traveling to conventions displace high-ish-end private tourists who then downgrade to 4* instead of 5* hotels, with another crowd of middle-class travelers on the occasional splurge pushed towards other hotels, until budget-conscious travelers and big families (for whom there are very limited accommodation in the city, at least in the traditional sense of big apartments with many beds etc) are priced out altogether of the major areas of interest.
Short-stay requires a minimum of 7 nights. The city policy is to push the really short-stay tourists into hotels instead of furnished apartments or AirBnB. Many new hotels are under constructions or expansion in Amsterdam. Bear in mind the number of annual overnight visitors in Amsterdam is 11 times its registered population, and the city is still a major commuter hub and global business center.
The ban on large parties is an attempt to crack down on what is a serious nuisance in residential areas: stag/hen parties or large groups of (mostly) people in their 20s-mid 30s coming from elsewhere in Europe on super cheap flight for a weekend of drinking and smoking all they can. It had became a "thing" for the too-old-for-college-too-young-for-parent crowd": people making Amsterdam their weekend alcohol/weed playground, thanks to EasyJet. There are several horror stories in the press on "out-of-control" house parties in rented out short-stay flats, which are obviously annoying to neighbors, and more difficult to police since - contrary to a hotel - there is no receptionist on site just to evict the worst offenders and call the police in the middle of the night if need be -.
I'm not in any way suggesting your group would behave that, just explaining the rationale of the regulations against large groups in residential areas.
Furthermore, social rent flats are now banned from being let out temporarily, fo real (under risk of eviction). There were a non-negligible number of flats, in particular in the Joordan, where long time social renters had just moved in with a significant other, or a relative, or a flatmate elsewhere, and then cashing in the short stay market for the allowed 90 days, such that it collected in 3 months more than enough to pay the rent for the whole year with cash to spare. The Joordan and the flats near Nieuwmarkt have many long-term occupants with rent-for-life rights (of sorts), people who moved there in the 1970s and 1980s as low-income professional but have some grandfathered rights to keep living there if they don't move out (while private rents are some 8-15 times more expensive than before the time these areas were run-down and best-avoided).
Practical solutions in your case: split the party, first. There are obvious economies of scale for 2 people staying in a room instead of 1, and usually some savings per capita for 3 or 4 staying in the same room. However, the supply of larger rooms is thin overall. Try searching for separate rooms, each accommodating 4, and check if that increases your options in your desired price range. I guarantee you that looking for a place to sleep 10+ will be difficult no matter where.
Second, consider staying in a city close enough to Amsterdam that you can easily take a train in and out, such as Zandijk, Haarlem, Hoofddorp, Utrecht, Hilversum, Almere, Lelystad.
