I recall some major US chain (TJ Maxx? JC Penney? Target? Something?) that decided to start pitching some kind of 'honest pricing' scheme, where all their stuff was just rounded up, so instead of $24.99 it would be priced at $25 flat.

A noble goal, but it apparently backfired on them spectacularly because of the same reason why retailers did that in the first place.

It was JC Penney, however they went beyond merely rounding prices. They ditched sales and coupons, which are unfortunately very popular, and that is often cited as the reason the "fair and square" plan failed.

Did they replace the sales and coupons with simply lower prices across the board? Because that would make it more attractive to buy there. If not, it's a price increase.

Yes, but the lower prices across the board were close to the average selling price before, not the best price you used to be able to get using a coupon for an item on sale. Therefore deal hunters no longer wanted to shop there. The price-insensitive folks still did, but they were the ones who used to pay full price and subsidize the deal hunters, and now they were getting a lower price than before. Thus it was a money losing strategy for the company.