I would do it using a transistor like a MOSFET, but the estimated high current makes it impractical due to too much heat.
Then all you need is a better FET. Look for ones with a low drain to source resistance when turned on. The lower this is the less power you burn when you switch it on.
If you think this is wrong then post your calculations as to how much heat your FET has to dissipate.
I don’t think you can dimm those constant current strips.