Six hours ago, the measured Vt for the altered BUZ11A was lower:

Factory Vt = 3.84 V, C = 2.69 nF
Modified Vt = 1.57 V, C = 2.99 nF
After 6 hours of rest, Vt = 1.64 V

I would like to say it's because of some temperature variations, but it looks like the transistor is slowly recovering to it's original higher Vt.
[DeepSoic] have similar results: https://hackaday.io/project/16384-enhancement-to-depletion/log/48018-testing-tolerance-to-switching-drive

So far, the self recovery seems to happen the same, no matter if the transistor is powered or disconnected.

Later edit:
2016-10-24 (one day later) Vt = 1.66 V; C = 2.93 nF
2016-10-25 Vt = 1.64 V; C = 2.92 nF; T = 27.4 *C
2016-10-26 Vt = 1.64 V; C = 2.90 nF
2016-10-27 Vt = 1.62 V; C = 2.92 nF; T = 26.5 *C
2016-10-28 Vt = 1.63 V; C = 2.89 nF; T = 26.1 *C
2016-10-29 Vt = 1.62 V; C = 2.91 nF; T = 26.8 *C

Not sure any more if any self recovery happens at all. Vt was stationary for the last 5 days. During all this time the transistor was not connected.