Why not just pay down your debt, and then work on getting cards or CLI on cards that you actually need and will use?
There's no need to stack CL on cards that are useless to you.
Your utilization percentage is just one of the many factors lenders look at.
For example, someone might have 50k income, owe 30k of credit card debt, and have 5% utilization. That is still going to spook the hell out of any lender.
JPMorgan Palladium (100k), AmEx Platinum (NPSL), AmEx SPG (46k), AmEx BCP (42k), Chase Sapphire Preferred (47k), Citi Prestige (31k), Citi Thank You Preferred (27k), Citi Executive AAdvantage (25k), JPMorgan Ritz-Carlton (21k), Merrill+ (15k), US Bank Cash+ (22.5k), Wells Fargo (12k), Bloomingdale’s (12.4k), Chase Freedom (5k), Discover IT (5k).