Effective alternative to water-resistant barrier behind siding?
The short answer is that there isn't an alternative that will yield an acceptable degree of effectiveness.  Vinyl siding is not intended to create a moisture barrier, and attempting to create a moisture barrier with it could potentially exacerbate the problem by trapping water underneath it.  This is almost always specified in the installation instructions (and almost always required by code). For example, in from the CertainTeed Vinyl Siding Installation Guide (my emphasis): 


  Vinyl siding is an exterior cladding; it is not a complete weather 
  resistant barrier. Before applying siding, make certain the substrate 
  is watertight. In order to be protected from precipitation, the 
  substrate may need to be properly flashed around areas such as 
  windows, doors, other openings and corners so as to shed water  to the
  exterior. See page 45 for proper flashing around windows.  The siding
  alone is not meant to be a watertight barrier.


Caulking only the J-channel is also not sufficient to prevent water infiltration. If you examine vinyl siding closly you'll notice that the bottoms of most siding pieces have drain holes, and runs longer 16` (depending on the manufactured length) will have unsealed lap joints.

If you seal all of these openings, you will likely still have issues. Vinyl siding is designed to allow air to move behind it to allow moisture out from between the vapor barrier and the siding.  Sealing it enough that it forms a water barrier would create a moisture trap behind it that could potentially be as bad as not sealing it.

Finally, vinyl siding is hung fairly loose because it expands and contracts quite a bit.  This means that you can either seal it well enough that the seals won't break due to expansion (which will make it buckle and warp) or allow expansion and contraction (which will break your seals and provide areas for water ingress).

Any "solution" is basically just going to mask the underlying problem or make it worse.  I'd say at this point it's a matter of weighing the long term consequences of not fixing the issue (mold, insects, rot, structural failure) with the short term costs.