Room ratios

I'm with Arthur - just install some corner bass traps in each corner (larger the better)

When you say each corner, do you mean all four?

I would build in soffits, soffit traps, corner traps, and use a Rives PARC. Those room ratios are going to give you serious bass problems and you will probably need to electrically correct, but don't do only that. Try to reduce the problem as much as reasonably possible first.

I would prefer to change the room size before adding any sort of electronic device to correct. Hence the question should I make the room 11.2' X 15.2', this is not difficult at all for me, just hope to best use my efforts towards good sound

If it was easy for me to convert one of my rooms to one of the recommended golden-ratio sizes, I'd do it in a heartbeat. Nothing, and I mean NOTHING beats great room acoustics. If you have a great room, even mid-fi gear can sound glorious.

The alternative of spending a lot of money on bass traps and expensive equalizers and getting worse results does not make sense to me, provided that you have the ability to easily alter your room dimensions to a size that will support relatively linear bass response. Most folks know that's the hardest area to get right.