I think I see what you are talking about. Many aluminum frames have
a, sometimes more than one, similar small lip, as that. I am
thinking: If there is just a small space between the sash and the
aluminum jam/frame, I would think some expanding foam would help seal
and shore up that contact area. If this is a reasonable option, make
sure all your alignments (level and square) are in place, before you
seal the sash with the expanding foam. If you are unsure about using
such a tight or secure (glue-like) foam seal, then "backer rods" may
be more comforting, for packing into that tight small spacing. Backer
rods are foam or foam-like rods (various diameter sizes, for packing
into small crevices, as that....1/16" or 1/8" is pretty small, not
sure if you can easily find a small backer rod for that size. I am
supposing the side and top fins are unable to be secured, as they
normally would be.

After reviewing all the pics again, and specifically the 3rd pic: I
had earlier mentioned removing the lower vinyl exterior face frame
molding. Maybe you have already removed the exterior molding, i.e.,
the aluminum one (the sill you cut out). Was there an exterior
aluminum lower face molding, similar to the vinyl one, that has been
removed OR was the sill, you cut out, also the lower molding (same
piece, 2 functions)? If so, then forget about removing the vinyl one
and consider proceeding, with the previous instructions regarding
moisture barrier installation. The new sill will have to have 2
functions, also, if applicable, relative to the position of the
previous aluminum sill (& face molding?). Does this correction
(backtracking) make sense? **If there is some confusion here, we may
need a picture of another intact aluminum window, with all the
exterior facings/sill in place, to see it's layout, especially the
sill, i.e., you mangled the bottom of the sill and had to hacksaw it
out, so we don't know, for sure, how the drip edge part, of the
previous sill, was positioned over (or in conjunction with) the
vinyl. Since we have to make a new sill, we may need to see an intact
window to get a perspective for a plan of fabrication and the
installation.

As long as you don't break those shingles into powder form (into a
dust form, able to be breathed in), you should be safe. If you have
to cut, trim, drill or otherwise break any of the shingles, spray
them, first and as you cut, with cheap hair spray (sticky stuff), to
prevent dust from flying. That kind of wetness (hair spray) won't
bother your wood, insulation, etc., nor your tools. Don't spray bare
wire/wiring areas.

Sonny