EXPERT RESPONSE
In theory, what you describe should work. A lot depends upon which Linksys router you're using. You may need to do a firmware upgrade; the first stop is Linksys Tech Support; describe to them what you're doing, and the specific model and firmware revision.
There are other options, though. You can use client bridges, which are client devices that have Ethernet ports, in place of the APs in bridge mode. Third-party firmware that turns APs into clients is available for some Linksys models; this might work for you but should obviously be used with caution. You can buy a point-to-multipoint (P2P or PTMP) bridge (available from a number of sources), or you could use a wireless mesh system (ditto). The big question is distance -- it may be that your endpoints are too far apart, and the connection quality is weak or broken. You might be able to use add-on booster antennas if that's the problem. Linksys sells a number of these.
I personally use client bridges in cases like these -- they're cheap, simple, and designed specifically for this application. Good luck!
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