What kind of headers are they? Are they those "stackable" ones?
Stackable headers come in two kinds: garbage with pins that are practically foil in one dimension, with rough edges an generally utterly awful build quality (you can feel as you plug them together that they're garbage!), and The Good Ones, with square pins (0.6mm in both dimensions), gleaming gold plating, and a delightful smooth yet solid feel as they are plugged together. Unfortunately, the two look nearly identical in the photographs that you have to use to assess ones offered on ebay/aliexpress. But I can give you two tips after finally meeting success after years of unsuccessful search for more of The Good Ones after having once gotten a single batch of them when I first got into the hobby: 1. ebay is almost all garbage ones, and 2. "EziUsin" on aliexpress, at least some of their listings are for The Good Ones (they put that name in the corner of their pictures, so search for stackable header, then look for that name in the pics) - they're also an all around great aliexpress store for pin header, for that matter; the other day I made a table of all the kinds of pin header (eg, straight, angle, single/double row, smd vs TH, etc) in 2.54mm, 2mm, and 1.27mm pitch, marked which ones I had, and went to fill in the gaps with the most affordable listings... and then realized that my whole order was from them....
If they're the crap ones, and they didn't come presoldered, well, you're kinda getting what you deserve for putting those headers into your boards instead of the trash can, which is the only place that the bad ones belong. Either get The Good Ones, or if you dont need stacking, just use normal male pin header.
As an aside, yeah, I've done the tinning of male header pins too... Some female pin header is just not very good. I prefer to use only male pin header and female dupont jumpers (male dupont connectors kinda suck, as does female pin header) - but the choice is forced on you if using Uno + shields.