The difference between an L and R is the L has two sets of counter weights on the crankshaft instead of one. Two is supposed to be smoother. Another thought, you could make it a Pponk since that needs the crank with two sets of CW's
I don't think this is correct.
Check the 470 TCDS, esp notes 4 & 5:
Note 4 says A, J, & R models have one 5th order & one 6th order dampers, where the K & L models have four 6th order dampers.
Note 5 says L is the same as K except for relocated carb & revised intake manifold oil sump.
http://rgl.faa.gov/Regulatory_and_Guidance_Library/rgMakeModel.nsf/0/b55509a1fd61c3ee862579530053a626/$FILE/E-273%20rev%2037.pdf
I'm not an A&P, an IA, OR a lawyer.... but IMHO you could reconfigure the L engine as a K, restamp the data plate as per the service bulletin Trent F provided a link to
http://www.tcmlink.com/pdf2/M75-6R1.pdf
note that conversion in the engine logbook,
and install the converted engine with a airframe logbook entry as per the 54 model specs (A J or K allowed) in the C180 TCDS.
Not sure if an engine replacement requires a 337?
A couple complications, already noted by others:
different engine mount, and different exhaust.
My 53 was converted to a K engine about 20 years ago-
they welded 4-bolt flanges on the original exhaust system.
and fitted the A engine's mount legs onto the K case so they could use the original engine mount.
These mods were field-approved on a 337 for my airplane.
FWIW I think biting the bullet and buying a later mount is a better idea--
the way the rubber mounts attach is much superior to the early mount IMHO.