Staircase tiling

Here's a re-ordering of the pieces from the example. It really doesn't matter how they are oriented as long as one uses the maximum number of the largest size pieces. I will discuss filling the rows one by one starting with the longest. The rest will be triangles filled in by smaller pieces.

$100/12=8r4$ which means if we fill the longest 5 rows with 8 copies each it will leave a copy of the n=4 staircase that will be filled by 4 small straights. Pieces used: $8*5+4=44$ and rows 100 to 96 filled.

The next 12 rows can be filled by $7$ copies leaving a n=11 staircase that will be filled by $11$ straights. Pieces used: $12*7+11=95$ Rows to 84 filled.

The next 12 rows can be filled by $6$ copies leaving a n=11 staircase that will be filled by $11$ straights. Pieces used $12*6+11=83$ Rows to 72 filled. Continuing

$12*5+11=71$ will fill to row 60

$12*4+11=59$ will fill to row 48

$12*3+11=47$ will fill to row 36

$12*2+11=35$ will fill to row 24

$12*1+11=23$ will fill to row 12

$12*0+11=11$ will fill the final 11 rows.

Total = $44+12*(7+6+5+4+3+2+1+0)+11*8=\boxed{468}$