N
TW
THR
TWLV
THRTN 
TWNTTW
TWNTTHR
NHNDRDTW
NHNDRDTHR
NHNDRDTWLV
NHNDRDTHRTN
NHNDRDTWNTTW
NHNDRDTWNTTHR
TWHNDRDTWNTTHR
THRHNDRDTWNTTHR  * 323: the 15-letter step
NTHSNDNHNDRDTWLV  * 1112 = NTHSND plus the 10-letter step.
NTHSNDNHNDRDTHRTN
NTHSNDNHNDRDTWNTTW
NTHSNDNHNDRDTWNTTHR
NTHSNDTWHNDRDTWNTTHR
NTHSNDTHRHNDRDTWNTTHR
TWTHSNDTHRHNDRDTWNTTHR
.
.
.
THRHNDRDTWNTTHRTHSNDTHRHNDRDTWNTTHR  * 323,323: 15 letters twice + THSND = the 35-letter step
NMLLNNHNDRDTWNTNTHSNDTHRHNDRDTWNTTHR  * 1,121,323 = NMLLN plus the 31-letter step
NMLLNNHNDRDTWNTTWTHSNDTHRHNDRDTWNTTHR
NMLLNNHNDRDTWNTTHRTHSNDTHRHNDRDTWNTTHR
NMLLNTWHNDRDTWNTTHRTHSNDTHRHNDRDTWNTTHR
NMLLNTHRHNDRDTWNTTHRTHSNDTHRHNDRDTWNTTHR
.
.
.
THRHNDRDTWNTTHRMLLNTHRHNDRDTWNTTHRTHSNDTHRHNDRDTWNTTHR  * 323,323,323: 15 letters thrice + MLLN + THSND = the 54-letter step
NBLLNNHNDRDTWNTNMLLNTHRHNDRDTWNTTHRTHSNDTHRHNDRDTWNTTHR  * 1,121,323,323 = NBLLN plus the 50-letter step
.
.
.
THRHNDRDTWNTTHRBLLNTHRHNDRDTWNTTHRMLLNTHRHNDRDTWNTTHRTHSNDTHRHNDRDTWNTTHR  *  323,323,323,323
NTRLLN...                                                                    * 1,???,???,???,??? = NTRLLN plus the 68-letter step


Hence TRLLN must appear in the 74th step of the staircase.   Now need to show there is at least one number with 74-letter name.

Note:
 THSND is 5 letters - its first appearance is 1,112
  MLLN is 4 letters - its first appearance is 1,121,323
  BLLN is 4 letters - its first appearance is 1,121,323,323
hence good guess for 74th step:
 TRLLN is 5 letters - its first appearance is 1,112,323,323,323?

Test: Add up the letters in 1 TRLLN 112 BLLN 323 MLLN 323 THSND 323 

323 (15 letters) x3 = 45
112 (10 letters)      10
N TRLLN                6
BLLN and MLLN          8
THSND                  5
total letters         74.