R-LWE instantiation with non-power of 2 polynomial
On the IACR eprint archive there is a paper entitled "Even More Practical Key Exchanges for the Internet using Lattice Cryptography" by Singh and Chopra that discusses using other cyclotomic fields which provide the same security guarantees as the power of 2 cyclotomic case.

One reason why these other cyclotomics are not as popular is that the speed of the Nunber Theoretic Transform in these other cyclotomics is not as computationally efficient.  Nevertheless as you point out there is a legitimate tradeoff between parameter sizes and computation.