It is fair to assume that iage is from the French iauge. Cotgrave [French-English Dict. 1611] gives clearly iauge/gage but it also seems that he chiefly understands a "gage" to be a measuring instrument and in particular "the instrument wherewith caske is measured" and not a joiner's marking or mortice gauge.
It is Cotgrave's habit to prepend joiner's tools with "a joyner's" as in "Gouge...a joyner's googe". His additional meanings of iauge might though offer a hint in the quest for a meaning that does not concern the marking gauge: "an yron Leaver; the soyle of ground; whence, Labourer à iauge. To plough deep, or as deep as there is any soyle". It seems possible that the "iage" refered to in the joiners/carpenters dispute of 1632 relates to the joiner's plough or plow especially in relation to item 9 "all Sorts of Wainscott and sealing of Howses and setling made by the use of Two Iages". Two plows, one twin-ironed and one single-ironed, were used from at least the early 15th century to produce the tongue and groove respectively of tongue-and-groove "setling" [settling/jointing together]. Where elsewhere the use of a single iage is alluded to, this could refer to an ancient but still used type of multiple board cladding where each board is continuously feathered or bevelled and has a groove on its unreduced edge only, so obviating the need for a plowed tongue. And it might also refer to lap jointing which also required one plane [rabbet or plow] only and was often used when laying floor boards. The relationship of iauge to the plow might be further supported by the early 17th century term "plough-jogger" or "-jagger" meaning a ploughman.
I do see that none of this dispels the possibility that iage means a marking gauge, not least because the French today sometimes call ita mortise gauge a mortaise jauge [although the word order suggests a later borrowing from English]English, and trusquin, also current, is a much older and the more widely used French term] and the action of a marking gauge is a ploughing action of sorts, but an iage as a specific type of joiner's [or carpenter's] plow/plough does seem to me to sit much more happily in the contexts it is found in here.