There are a couple of things you might keep in mind. The first is that this coiled up coax is not a balun. Most people call it a bauln, but it isn't one, it does nothing that will convert from a balanced to unbalanced condition.
It is a 'choke'. It can/does affect the currents on the outside of the coax. It doesn't affect anything on the inside of the coax, other than change the total length of the feed line.
So why the change in the 'match'? Beats me, about all I can honestly think of is that it has to do with the length of the feed line. That ought to give you a hint of two anyway.
Not being sure of what the diameter of that coil is, can you really bend LMR-400 that much? My experience with LMR-400 is very limited and coiling it wasn't part of that experience. There's several different 'kinds' of '400, but anything as small as a foot or so, seems like it would be sort of tight, you know? That tightness of the coil depends entirely on the coax being used, there's no set, or 'standard' diameter for a choke, and until it gets really huge, the diameter really doesn't make a lot of difference. What's used as the coiol form is usually decided by weight more than anything else. If it's ferrous just would mean the choke could have less coils and the same inductance. Depending on how/where you do that, it might be a better solution, wrapped around a mast, for instance. (Beside the point, but I have a choke wound on the mount of a mobile antenna, big mount, little too much feed line, just worked out as a handy place to 'save' it, sort of. Haven't had any problems yet. Uh, no, isn't LMR-400.)
And just to make everyone's day...
All those PL-259's, SO-239's, double-female, double-male, connectors are not 50 ohm devices. Isn't that thrilling to know!? What their actual impedance ends up being is always a matter of how well they are assembled and the particular coax they are used on. There will almost always be an impedance 'bump' (very small one!) at any UHF connector put in the feed line. I'm not sure, but I think an 'N' connector, and maybe(?) a 'BNC' connector are supposed to be 50 ohms, but not a UHF connector (PL-259, etc.).
Does that mean I think you should run right out, buy 2 or 3 hundred 'N' connectors and change everything around you? ONLY if I get to sell you those 'N' connectors! Or in other words, no, I don't. It just won't make that much practical difference at HF, especially on 11 meters. (You don't wanna know what happened the last time I tried putting an 'N' or 'BNC' connector on a feed line, and I'm too embarrassed to volunteer it!)
- 'Doc
Having 'made your day', I'm going to the lie-berry and find a good book... and having made several 'edits' to correct spelling, I give up. If you find a few it just means I didn't.