Alex and Weinmann do make some decent and affordable 27" rims -- I'm using Weinmann LP18's on my old Peugeot -- but it's not quite that simple. You'd need to disassemble your current wheel, removing the spokes and nipples. You could then transplant a new rim, but you'd need to make sure the spokes are the correct length for the rim. Different rims, even if they're made for the same tire size, may require spokes of different length. You'd need to replace your current rim with one of equal ERD (effective rim diameter), otherwise you'll need new spokes in addition to a new rim. And by that point, if we're talking about budget rims, you might as well buy a new wheelset because rims plus spokes may not be that much less expensive than pre-assembled wheels, and that's before considering your time and aptitude.

A new alloy 27" wheelset with Weinmann LP-18 double-wall hooked rims and stainless spokes costs a little under $100 from Niagara Cycle (link HERE).

...or you can run tires that have sufficient width to be used with lower pressure, which should keep 'em from blowing off your straight-sided rims.