You have been given advice by several members here that would solve your problems... initially your problem does stem from trying to use a paper for which there is no profile provided and soft proofing with a profile that is made for a matte paper. For the process to work using profiles then you NEED the profile for that paper and your printer/ink combination.
The only way you may get a print that is anywhere near being decent is to decide which OEM paper closest matches and letting the printer manage the colour, this is however far from ideal...
Messing around in a colour managed workflow when there is no colour management is a path to failure and no one can advise you... the only advice is to use paper that has a profile available for your printer/ink combination and that translates into 'buy better paper'.
Buy better paper does not mean more expensive, people like Paper Spectrum are reasonably priced and supply profiles for their papers and even if in the long run the paper is more expensive just think how much you will save by being able to do the job properly and not throw away 15 crap prints !!!!!