EDITED, BASED ON RECENT REQUEST...
... Drawer slides: suggest you find out carefully why they're sticking in the first place. Lubrication might help, for example a bit of candle wax or talcum powder can work very well (not both together!)
I'd suggest that re-routing is a bit heavy-handed, never mind the possibility of ruining the drawers. \First have a REALLY good look at the problem - check things for straightness, clearances, etc.. See where the wear marks are.
Then perhaps ease the runners with fairly fine abrasive, clean and lubricate as discussed.
If you're completely stuck, you're in Bristol, so PM me.
E.
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The POF 600 is now my go-to for 1/4" and 8mm work, with a Trend T11 for heavy stuff (it lives in the router table). I also have a Power Pro (I think) from B+Q. It's 1/2" but really cheap and nasty - the depth stop no longer locks properly, and it's prone to random speed changes. Currently in the attic - must get around to throwing it out.
My first was the POF500, which I have as a spare and has been incredibly useful down the years. I recently got a POF600 from the bay, which is the variable speed version (otherwise identical). The old Bosch ones (20+ years) have rock solid Swiss-made motors and bearings - dunno about the present generation - and will take the fences from Trend routers too. Trend's nice, micro-adjustable fence is hardly ever used on the T11, but it was designed to also fit the T4/T5, which have the same bar spacing as the Bosch. The bar diameter is different, but... the bars from my Power Pro fit the fence so it can be used on all my routers