Floor heating, eh? Eeeh, luxury!
You could use plates as you suggest, but 12mm or better 16mm thick, then rather than trying to weld studs to it, which mean lifting the mill that much further, drill and tap M12 or M16 holes in them to take studs.
Make the studs of correct thread length, or use stock studding but put a dot of weld on it, to prevent it winding down into the wooden floor.
However, such plates would need be very wide to remove the tipping hazard. So really, channels or square-section tubes projecting away to the sides of the machine are the better option, but do consider these may present trip hazards. You could join their ends with cross-members to form a rectangular frame, which will be better and safer. Since their joints are taking very little load the welds don’t need be to shipbuilding standards, though you could use angles and bolted joints instead.
To provide for bolting the machine to a frame made from tube, it may be feasible to bolt heavy-duty angles to the inside faces of the longitudinals, to give ready access for the fastenings. The main load is on the tube, the nuts and bolts basically hold everything together against spreading. This needs the base bolt-holes far enough in from the edge of the base of course.
Another option is to screw thick plates or flat bars to the tops of the tube, drilled and tapped through into the tube, then the bolts go down through the machine base to screw into the plates.
How to screw these bars to the tube so you don’t have their heads below the underside? The method I used for securing my workshop’s hoist columns, of 50 X 50 X 3mm steel tube, to the wall was to drill right through for the masonry fastenings, then use a cone-drill to enlarge the outer holes to pass a socket to engage the screw-heads, leaving the fastenings neatly concealed within the tubes.
You could indeed develop this principle to use cylindrical cross-hole nuts (which you’d have to make specially) held in the full-diameter cross-drilling, rather as some furniture fastenings work.