I am a firm believer in using a chemical to remove the slime, but many people on the board disagree - that being said I would choose one of two ways -
1) Chemical - with Red Slime remover or Chemipure
2) Mechanical - during water changes, siphon out what you can and let the cycle take it's course - it will eventually go away once the nutrients for it are gone.
I would leave it for now. Your tank is going through the normal cycle. I had a huge read slime problem in the beginning. It took about 2 weeks but it eventually did its thing and left. Hopefully forever!
red slime remover is just an antibiotic. That being said, it's use on such a new tank may cause more problems than it solves, by killing off the bacteria the tank needs along with the slime. Slime remover isn't a 100% guarantee and only treats the symptom, not the cause of the problem. In some cases or even from improper use you can end up with a strain of slime that is especially resilient to the antibiotics or maybe immune. I have found that in treating red slime it is better to attack it's causes rather than the slime itself. The most common cause of slime I see is a lack of flow (GASP, not me. I have 35 PHs placed strategically throughout the tank!?!?!?!? ( well, maybe you needed 36 this time or you missed a spot). The lack of flow allows detritus to settle or nutrients to build up and feed the slime which then has a chance to settle and spread easily since it is also photosynthetic. Try adjusting returns so they spread flow more evenly or if your return is "Y'd" try removing one of the sides so it is just a single. The increased flow will make it a lot harder for the loosely attached slime to gain and keep a foothold on the substrate. I used to use the slime remover and it usually worked really well but it's approach to the problem is flawed. Your Tech Tank has slots along the plastic euro bracing that can be used for creating closed loop systems so you don't need to add the PHs directly in the tank. If you can do a water change and remove as much slime as possible and increase the flow somehow I guarantee you that you will see the slime disappear over a few days. No need for the removers.