So, you've cleaned the capping station and it is still wicking ink - then the capping station may just be too old and swelled and making contact with the bottom of the print head. That's not ideal to be sure. I am not certain that there is a remedy for that other than replacing the capping station.
The refillable carts vents are much wider than the OEM. So the ink is just going to drop if the head is making contact either directly or via moisture. There may be something to trying to close the vents off to try and match the OEM. But, that would be a matter of experimenting. The OEMs vent through a very tiny channel. There may be a possibility that the capping station is not swelled from age but instead the drain tube is not draining and needs to be cleaned. It could be that the capping station is just remaining excessively moist and this is why the heads are draining. If the prime is being interfered with - this can be the source of the overall banding. Wicking can produce air in the ink channels.
It's a question perhaps, of how far do you want to go down the rabbit hole with this printer? The R2400 was discontinued here in the USA about 8 years ago and replaced by the Epson R2880 which of course was replaced by the R3000 now too replaced recently. And I am guessing that you probably have not done any component replacements on this printer and will not want to because of costs vs age of printer. So age may be the limiting factor of this printer.
If you're serious about Piezography, you should be doing it on the best condition printer you own or can find. It's a very high performance system and it depends upon you to supply the hardware and operate the software correctly. Here in the USA you could have completely refurbished an R2400 last year for $93.90 which would get you the pump, the capping station, and a wiper. But, Epson just recently stopped support of this printer, the 7600, 9600 and 4000. (7 years since discontinuation.)
You can still buy a refurb kit for an R2880 for only $48.78. So you might want to return your 2400 to color since it works with the OEM carts still. And get a good used inexpensive R2880 and hope for the best that its been well maintained. If the print head works when you test it - and all nozzles are firing true - you can refurbish the clean station when you need to for under $50. But you may be able to use it as is.
(go for cleaning the tubing from the drain system - it's worth a shot for sure!)