I'm assuming that the problem is with the noble's outfit (I never noticed the sentence before the "first outfit is free" sentence on PHB 131, so...). I'll just drop that outfit and pick up a courtier's outfit (30 gp), which should have this happen:
160 gp starting
160 gp traveler's outfit (free)
135 gp studded leather (25 gp)
115 gp rapier (20 gp)
85 gp shortbow (30 gp)
84 gp 20 arrows/quiver (1 gp)
82 gp dagger (2 gp)
77 gp common lute (5 gp)
75 gp backpack (2 gp)
74.9 gp bedroll (1 sp)
64.9 gp bottle of fine Deluene wine (10 gp)
59.9 gp spell component pouch (5 gp)
57.9 gp belt pouch (1 gp)
27.9 gp courtier's outfit (30 gp)
22.9 gp signet ring (5 gp)
2.9 gp alchemist's fire (20 gp)
I'll update the sheet right now.
Best,
Nick