OK. A bit messy.

Please ignore those n-gram counts. I didn't mean to include them.

深み	1,091,528		
深味	8,593

I don't think we can. 味 isn't ateji for those senses.
I'm not really comfortable with [uk] on senses 2 and 3 given that they're never written as 味. Perhaps it's time to stop using [uk] on entries like this. Sites/apps have had long enough to add support for sK/sk.

@@ -30 +30 @@
-<s_inf>as ...み...み; after the -masu stem of verbs with opposite meanings or after a -masu stem and a -zu stem</s_inf>
+<s_inf>as ...み...み; after the -masu stems of verbs with opposite meanings or after the -masu stem and -zu form of the same verb</s_inf>

We already have 味/み as entry  2258680. 
- 味 [み] /(n) (1) (sense of) taste/(suf,ctr) (2) counter for food, drink, medicine, etc./
Merge?

gg5, prog, luminous, daij

Wiktionary has "place" for sense 2, which I think works better than "-ness" or "-th".
smk tags sense 3 as〔雅〕. Meikyo tags it as〔古〕.

@@ -3,0 +4,4 @@
+<k_ele>
+<keb>味</keb>
+<ke_inf>&sK;</ke_inf>
+</k_ele>
@@ -9,3 +13,6 @@
-<s_inf>nominalizing suffix, esp. of sensory or subjective adjectives; also written with the ateji 味</s_inf>
-<gloss>-ness (as in sweetness)</gloss>
-<gloss>-th (as in warmth)</gloss>
+<misc>&uk;</misc>
+<s_inf>after an adjective stem; nominalizing suffix indicating a quality or feeling; also written with the ateji 味</s_inf>
+<gloss>-ness (as in "sweetness")</gloss>
+<gloss>-th (as in "warmth")</gloss>
+<gloss>a touch of</gloss>
+<gloss>a tinge of</gloss>
@@ -15,3 +22,3 @@
-<s_inf>nominalizing suffix indicating location</s_inf>
-<gloss>-ness (as in deepness, weakness)</gloss>
-<gloss>-th (as in depth)</gloss>
+<misc>&uk;</misc>
+<s_inf>after an adjective stem; nominalizing suffix</s_inf>
+<gloss>place</gloss>
@@ -21 +28,3 @@
-<s_inf>as ～み...～み</s_inf>
+<misc>&poet;</misc>
+<misc>&uk;</misc>
+<s_inf>as ...み...み; after the -masu stem of verbs with opposite meanings or after a -masu stem and a -zu stem</s_inf>
@@ -22,0 +32 @@
+<gloss>sometimes ... and sometimes ...</gloss>