Welch, that is not necessarily true (not that it isn't, it may well be), because paper has changed a lot, specially in the last years as inkjet printers are not so demanding and makers have switched to lower quality and cheaper pens to increase their margins.
My own experience (and I do not use checks, I speak of just writing) is that paper has gone down noticeably in quality. I still have 'old' paper (from 40+ years ago, from before even A4 was in use) and believe me, there is no comparison. Even lint rich paper from then was far more friendly than modern copy paper.
As ofr the OT, I think that a small clarification is due: writing is the result of a combination of three main factors: pen, paper and ink.
Regarding pen, one thing to consider is that Eastern (mainly Japanese) nibs use a thinner standard in nib size than Western pens. Thus, a Western EF will usually write like a Japanese F or even M. Conversely, using a Japanese EF pen may result in a line like that of a Wester EF turned upside down (i.e. much thinner). So, using a Japanese EF may be a solution.
As for ink, not all inks are born equal, some have more or less surfactants (spread more or less on paper). In the good old times, there was not much choice and it was easy to give advice. Nowadays, the options are huge. I think that Arkanabar has summarized them rather well, at least to mention some of the more popular options.
As for practical advice: if you have a Pilot EF, I would first try that and see if it solves the problem. That may be the cheapest and quickest (specially given the current situation) solution.
I would be wary of getting started on the ink testing rabbit hole. Once you get started you may never end your quest for "the best" ink for you. Instead, and considering current confinement situation, I would take advantage of it to read as many reviews of some of the inks mentioned by Arkanabar as possible, and then make a decision for one of them and go for it.
Ideally you should test it first to avoid buying something you end up not liking, In the good old times it was easy to go to a brick and mortar (B&M) shop and ask for a dip test. Since you get your own paper, it should be easy to bring a sample sheet to test it... but FWIW, B&M shops are rare now in the US, so this may not be a solution. You may want to order some sample (2ml) vials from an online seller (like Goulet, JetPens or many others) to try first. The idea is to avoid ending -like many of us- with a large collection of inks you will never be able to use up in your whole life.
Generally speaking, many traditional blue-black (BB) inks seem to be permanent, iron-gall based (Pilot, Waterman, Pelikan, Montblanc...) and well behaved, many Noodler's inks have been designed to be tamper-proof with checks and legal documents in mind (personally I know X-Feather and am happy with it), and then there are lots of permanent inks to try (I would use a permanent ink for checks to avoid tampering). When looking up reviews, the magic words are "Document" (or "Dokument"), "Registrar", "Iron-Gall", "Nanoparticles", "Permanent" and the like. Just search the net for reviews, look at pictures to get an idea of the colors and at the comments to see how good (for your purposes) they are.
And finally, as already mentioned, you can try diluting the ink. Most inks are oversaturated and diluting then (sometimes a lot) will still yield a readable line. If you decide to do that, do it first on a small amount in a separate vial (e.g. an Eppendorf test tube) to avoid spoiling a full bottle. Depending on where you live, you may be able to use tap water, but it is usually deemed safer to use distilled water. Just take a small syringe to measure say 1ml ink and 0.1 or 0.2ml (or maybe more) water, pour on a vial, shake and tr.