Binedave,
We are non-EU, so while on B permits we were restricted to living in the canton that issues my husband's work permit. However, if you are EU I believe those restrictions do not apply, and you are free to live where you choose. Do confirm that with the powers that be, though - I'm not fully up to date on Eu perks.
Housing in Ausserschwyz (March, Höfe, easily commutable to ZH) isn't necessarily that much more expensive, unless you are looking for a mansion.
Most towns in the area have a range of housing from flats (small to luxury) to older or 'normal' homes, to eye-popping villas. Yes, those villas will be priced up in the stratosphere, because all those ZH tax exiles are chasing after the handful of mansions available.
But some 'normal' properties are actually quite affordable, especially when you consider the tax advantage. We bought a small older home, nothing fancy, in need of renovation - for about what a similar property in the Pfannenstiel area would have cost.
Take a look at the Homegate site to compare housing prices in various areas, and run through their tax calculator - you may find, depending on your individual situation, that the tax difference more than makes up for higher prices.
I would caution you, however, to research the housing market in CH and in the area before buying - it isn't like housing in the US or UK. Generally, houses have appreciated very slowly, and the market moves at a snail's pace.
Buying a house in three months might be unrealistic. It took us a year of looking before we found our home, as not too many properties come on the market at any one time. And, once we found our place, we had to move heaven and earth to get the sellers to agree to closing in three months - six months or longer from signing the reservation contract seems the norm here. You might get lucky, but do be prepared to be flexible.
There are several threads detailing the oddities of home purchasing and ownership in Switzerland - do browse through them.
I love living out here - it was definitely the right move for us.
Best of luck with your move.