Specialty home "Turkish" and "Greek" hand coffee mills ARE burr grinders.
The big supermarket machines that do Koukouvagia's Greek coffee are burr grinders as well. Also, she just might possibly maybe know something about the subject.
If your electric, burr "espresso grinder" is at all good, it should not have any problem grinding for an ibrik. The finer you grind, the greater the tendency to clog up the burr.
The solution... wait for it... is to clean it now and then. Preferably by disassembling, or using something like Umex Grindz grinder cleaner; but even shooting a little bread through it will make a positive difference.
Getting rid of the rancid oils which stick inside every burr grinder is going to make a huge positive difference in your coffee -- no matter how fine you grind and how you brew.
With all due respect to Suzanne, a propellor grinder is about the worst possible way to make fine ground coffee -- because of the heat inevitably generated and the inconsistency of the grind. A lot of folks, including me, say it's okay for coarse ground as for a "French press," or to do a medium grind for a not-very-revealing brewing method like a paper-filter, pour-over. But your Xtreme java maven is likely to insist on a burr grinder for everything.
BDL