While both things you mention are possible, it's important to note that I've only cleaned the sand twice. And the first time was in response to the algae on it. So cleaning it did not start the problems. Not sure if it is making it worse though. But I suspect not.
Man, this is a topic I'm passionate about. I've got three types of fert pump; Aquamedics, Mityflex sold by AquaticEcoSystems.com, and a DP1-DT from AutomatedAquariums.com. The Aquamedic are all plastic and junk IMO. The Mityflex is much sturdier, but waaay to expensive and very noisy. But the little pumps from AutomatedAquariums.com are just right. And they come in a number of flow rates.
And FWIW, you can see
on this page, these are virtually identical to some of the pumps advocated by other people here, just a bit more expensive. But I get them from AutomatedAquariums because they package them in
these nice boxes.
IMO don't waste your time with variable flow pumps. You want to buy it according to the flow rate you need, install it, benchmark the flow after it is installed, and then you can always plan on that rate - adjusting timing as needed. Doing guesswork over speed on the variable flow pumps is nuts IMO.
As far as flow goes... I need about 3.5 ml/minute for my K2SO4 stock, but generally between 0.5 and 0.75 ml/minute works well for micros. For KNO3 and KH2PO4 solutions I think you are best off at around 1.0 ml/minute. All of these will have you dosing between 5 and 60 minutes a day... depending on your uptake rates. But they give you an nice granularity - easy to nudge the timing up or down a bit as needed. If you get something that flows too fast, you wind up with something that a 1 minute increase or decrease is too much or too little.
Also, be sure and not buy anything with 1/32" tubing connections. Too tough to adapt to airline hoses (which I use for long runs to the fert injection point).