I do it a little differently, too.
I check my foundation is square for a start (on an artist's cutting board) and then rely on this for frame squareness. Wax dimensions are more important with the bigger format frames. If it not square one side, it is not too much of a problem (a simple trim hopefully) - not square on both sides and it is a bear with bee space at top and bottom of the box (foundation has to go in with a gap at one end of the top bar, so the loops are not all bent level with the edge).
As vid, remove wedge and clean up both top bar and wedge, also any roughness in the top bar shoulders. Takes very few seconds and worth the time (I only use 'seconds' frames from Th*rne).
I then fit the side bars and one bottom bar, only nailing it at one end. The bottom bar chosen, is of course, the opposite side to the wedge, not the same side (BTDT). With it as square as possile nail the shoulders after bedding down with a thumper, as in the vid.
I then bend the wire loops on my foundation and lay it across the frame. I insert one edge in one groove and gently bow the sheet to slot the other end in, adjusting the free end of the bottom bar for a snug fit in the grooves. I then fit the other bottom bar (it will bend sufficiently to get around the stub ends of the wires). Then I nail up with the nail gun. 16mm brads are fine all round with shallows, but I am more generous with the 14 x 12s - four brads in the wedge and 19mm brads in the shoulders (plus, this year, 2 x 25mm 'on the tosh' down through the top bar at each shoulder). The 4 extras downwards are a trial this year on some of my big format frames and I will see if they improve the longevity or not (14 x 12s full of honey are heavy and have sometimes pulled apart if well 'glued' into the box or if dropped at all on a dodgy lug (usually outside the hive, I might add). So this may be a trade off between weakened lugs and loosened shoulders.
For shallows I have been known to use 14mm staples for both bottom bars in one go.
Some of my bottom bars are tight and some loose (seconds again!). I select a tight batch for the first bottom bar and use up any loose ones I come across, at the earliest opportunity.
Other tips are to snip off the corners of the foundation, if required, for an easier fit - particularly useful if the grooves don't quite line up (those seconds again!).
Certainly agree with Steve Dyer's points 2 and 3. It is definitely stronger cross-nailing bottom bars but it is not needed and a real bear to recycle the frames. IF you go for replacing frames rather than recycling, then it doesn't really matter a jot. Even 14 x 12 frames, with wax fitted, were less than £1.90each, this year, as I recall. But I don't buy 10 at a time!
RAB