My first theremin was a modded Jaycar, namely a Kees Enkelaar theremin, with his own custom mods, now out of production, then about half the price of an etherwave. (This part of the market is now catered for by Dan Burns.) I had a lot of fun with my Kees, and have witnessed Lydia Kavina wrangle a more than acceptable melody out of it, so it is possible, but not for the likes of me!
There are four aspects to playability; size, linearity, smoothness and stability of the pitch field.
Both my Kees and my etherwave can be tuned to an optimal pitch field size. The size of the pitch field is limited by the position of the volume hand, so, as you propose, the Jaycar will benefit from a longer enclosure.
My third "theremin" is a Japanese toy, similar to the White Stripes theremin mentioned recently on the Theremin World news page. Despite not having a volume loop (hence the quote marks) the circuit cannot be tuned to a field larger than six inches, which puts the notes so close together as to be unplayable. Naturally I love it, and have used in on an album track (with the shameless use of pitch correction and numerous effects.)
Linearity tells us how well a similar hand movement will produce a similar interval at different parts of the playing field. Typically at higher frequencies a non-linear theremin the same movement will produce a larger change in pitch. All existing theremins are non-linear to some extent. My Kees does not score well here, even after some tweaking by Fred Mundell (who posts here occasionally.) The wisdom many good players offer is that good linearity is desirable.
However one should note that the tVox Tour, the theremin of choice for Lydia Kavina and Barbara Buchholz amongst a few others is not particularly linear. Lydia has said at one of her masterclasses that I attended that this is not such a problem, and that she will move her body into the field to stretch the higher range, or further from the theremin to compress the lower range. (Thereby compensating for the non-linearity in a way that allows her not to extend her arm a long way to play high notes which would incur a loss of precise control.)
Thomas Grillo has advocated on youTube a technique of moving the arm towards the pitch rod along a curved path which will alter the angle of attack of the hand to the rod, so that the same hand movement will have a reduced effect (by changing finger movements from horizontal towards vertical) in the more compressed part of the pitch field. I am not qualified to comment on the efficacy of either technique, so am not doing so.
There is a limit to how much a player can compensate for non-linearity. The very worst circuits (such as my third "theremin") are so non-linear as to make compensation techniques insufficiently effective.
By smoothness I mean that if one were to plot a graph of pitch to distance from the theremin field (so that a perfectly linear theremin would give a straight line, and a non-linear theremin would give an exponential curve) then a smooth field would give a curve that looks like the graphs you find in maths text books at school, and a non-smooth field would appear more as if it were drawn by a small child whilst riding a horse with a limp that was galloping through a recently ploughed field. Top notch theremins score well here. I am not so sure about my Kees, and will leave it to someone else to comment upon it. My guess is that it is OK, but not in the top league.
By stability I mean the tendency for the oscillators to wander, causing the frequency of the fixed pitch oscillator to vary over time, and the variable oscillator to give different responses to identical hand and body positions over time. Clearly a more stable theremin is preferable to playing on shifting sands. This is easy to test - give your theremin a good warm up time so that it gets to maximum stability (exactly how long rather depends on your ear - typically better classical players report longer warm-up times - my Kees takes a much longer time than my etherwave) and then tune it to zero beat in an empty room and wait for it to start making a low note of its own accord. Again my Kees performs significantly less well than my etherwave here.
Also despite extensive attention by Fred, the volume response is nowhere near that of the etherwave in terms of usability. The Kees is good for staccato, but not legato. This is, in my opinion, as important a factor as the usability of the pitch field. You want your playing to have expression just as much as you want it to be on pitch. (In my case, far more so! Melodic playing is not my thing.:-)
I was content with my Kees for about a year, until I had opportunity to try an etherwave, when I knew that I had to own one, both for the timbre and for the playability. Since then both my Kees and my etherwave have been modded and tweaked by experts (the etherwave by Thierry) and while both are very much the better for it, the same comparison stands - the Kees is the lesser of the two instruments in many ways. I keep it because it has a couple of timbres not available on the etherwave, and because it is good to have a spare theremin.
I should add that I am not an expert. I have a dilettante understanding but nothing more, and am always happy to have my misconceptions corrected. If you know anything I say to be inaccurate please let me know, otherwise I will just keep on spouting wrong information and inadvertently misleading people.