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(2 edits) (+2)

https://imgur.com/a/PDjOJ4m (There is one unmarked grass tile in the bottom right)

It appears that there are in total
27+21+22+
30+68+82+
185+30+96 = 561
brick wall tiles and
39+56+101+
28+62+45+
0+58+34 = 423
grass tiles. These total to 5472 hunger.

In addition to these, there are 

33 tier 1 gems, 4 tier 2 gems, 1 tier 3 gems, 3 tier 4 gems, 6 tier 5 gems, 1 tier 6 gem, 2 gems of tier 7 and 8 and 1 more of tiers 9 through 12.

 When we merge gems we get the following payouts
1,2,4,8,14,23,32,41,50,... and so on, increasing by 9 for each subsequent tier. Therefore, as the brick walls merge into tier 5 gems, we should receive
(423+33)/2 = 228; (228+4)/2=116; (116+1)/2=58; (58+3)/2=30; (30+6+423)/2=229; (229+1)/2=115; (115+2)/2=59; (59+2)/2=30; (30+1)/2=15; (15+1)/2=8; (8+1)/2=4; (4)/2=2; (2+1)/2=1.

The payouts are thus 228*1+116*2+58*4+30*8+229*14+115*23+59*32+30*41+15*50+8*59+4*68+2*77+86=11635. Substracting the hunger, we should be able to get 6163

(5 edits) (+1)

I've managed this score, lower I think due to inefficent gem placement next to this east wall. So I'd think the 5088 is indeed the maximum, maybe can be pushed up to 5090 but not much higher. The main source that can be optimized is this upper-left puzzlebox



I have managed to extract everything from it save for these three grass tiles. Nothing is theoretically stopping it from having a better solution. I have then merged the 1-gem in the corner with a leftover from somewhere else