I'm not entirely sure how I'd go about spoilering this, so I apologize to anyone who stumbles by.
Working out the upper end in reverse was very helpful for finding a solution, before I'd done that, I had tried about half a dozen things, after solving all the forced moves possible there, my second try made it work.
/(1)\___
\44_/ 1 \
\43_/
/ 1 \___
\42_/ 2 \
/ 2 \41_/
\40_/ 0 \___
/ 2 \39_/ 0 \
\31_/ 1 \38_/
___/ 2 \32_/ 2 \
/ 0 \30_/ 2 \37_/
\29_/ 2 \33_/ 2 \
___/ 1 \28_/ 2 \36_/
/ 2 \27_/ 1 \34_/ 1 \
\19_/ 1 \26_/ 2 \35_/
___/ 2 \20_/ 1 \25_/
/ 0 \18_/ 1 \21_/ 1 \
\17_/ 2 \22_/ 0 \24_/
___/ 1 \15_/ 1 \23_/
___/ 2 \16_/ 1 \14_/ 0 \
___ ___/ 2 \_6_/ 2 \11_/ 0 \13_/
/ 1 \___/ 1 \_5_/ 1 \_7_/ 2 \12_/
\_1_/ 1 \_3_/ 1 \_8_/ 0 \10_/
\_2_/ \_4_/ \_9_/