Geshe Gyaltsen passed away in 2009. This discussion has lasted long enough that, we're he still alive, I'd drive down to see him and get clarification. If at some point I can access a geshe in my area, I plan on doing just that, but I'm not flying off to India in a panic.
I have had detailed discussion with a Geshe many times comparing the Sakya presentation of freedom from extremes with Tsongkhapa's presentation. Never has it been considered that Tsongkhapa might have a position of not holding any views. In LRCM Tsobngkhapa says,
Some [Tibetans who claim to be Madhyamikas] do not distinguish utter nonexistence from the absence of intrinsic existence, and do not distinguish essential existence from mere existence. They hope to avoid falling to the extremes of existence and non- existence simply by saying, "We do not claim that things are nonexistent (med pa); we say that they are not existent (yod pa ma yin pa). We do not claim that things exist (yod pa); we say that they are not nonexistent (med pa ma yin pa)." This is nothing but a mass of contradictions; it does not in the least explain the meaning of the middle way… Evidently their position is an overly literal misunderstanding of Madhyamaka.
I think your quote from Three Principle Paths is very interesting as it does say སྟོང་པ་ཁས་ལེན་བྲལ་བ (emptiness is devoid of theses) however it is only one quote and as Tsongkhapa responds when asked why Nagarjuna in the Vigrahavyavartani makes the famous statement about Madhyamikas not having theses and no positions:
"since there are also many passages that state that it is necessary to posit assertions, how can simply citing that one passage prove that Mādhyamikas have no positions?"