Despite several sources & specifications stating it is impossible, I have an HDMI output connected to a Dell U2711 DVI input at 2560 x 1440 via a simple HDMI to single link DVI-D cable, because the Dell U2711 accepts single link ~340MHz HDMI on the DVI-D inputs.
Unfortunately, manufacturers don't seem to actually tell anyone if a display has this capability - looks like the Dell U3011 and Philips 288p6 do as well. Good luck confirming this on other monitors.
Here are the lines you have to read between to figure out what is going on:
With some limitations, HDMI and DVI are the same signal. DVI uses dual link (more TMDS pairs) to get higher resolutions, while HDMI ups the per channel throughput with higher cable specs.
An Apple HDMI support article tells us that "MacBook Pro (Retina, Late 2013 and later)" support 4k (3840 x 2160 x 30Hz, 4096 x 2160 x 24Hz) on HDMI. This means 2560x1600x60Hz can work and probably will.
But HDMI only has pins for a single DVI link (4 TMDS pairs), so even if the DVI end of a cable or adapter shows the extra pins, it's still single link, and as everyone knows, single link DVI only goes up to 1920x1200x60Hz. Right? Except...
"... many devices output HDMI over a DVI connector [..] and some multimedia displays may accept HDMI (including audio) over a DVI input." (Wikipedia HDMI article)
A hint! I found confirmation on a random product page on amazon:
"Note 1: Resolutions above 1920x1200 60z require monitors to support DVI-D single link speed of 340MHZ, such as Dell U2711 & U3011 and Philips 288p6."
("active" Mini Displayport to DVI adaptor)
DisplayPort (vs HDMI) still applies here: the adaptor will only work with our "special" monitors, because the DisplayPort++ dual-mode (as in LVDS or TMDS, not dual-link!) version 1.1 transmits a single-link HDMI/DVI signal well above DVI single link specs, just like the HDMI output on my MBP.
By implication, DisplayPort to HDMI at high res should work, but clearly doesn't a lot of the time - searching Amazon for "DisplayPort to HDMI 4K" shows cheap cables and positive anecdotes. And DisplayPort to DVI-D single-link might work at higher resolutions if you have a monitor with this well-hidden beyond-spec feature, instead of having to buy the expensive converter to split it into 2 <165MHz dual link DVI channels.
Thank goodness for standards!