WWW hits and images indicate that 木板 mainly refers to pieces of wood and 木版 to woodblock printing.

I've backed off a merger.

@@ -9,0 +10,3 @@
+<r_ele>
+<reb>きいた</reb>
+</r_ele>
@@ -12,0 +16,6 @@
+</sense>
+<sense>
+<pos>&n;</pos>
+<xref type="see" seq="1641990">木版</xref>
+<gloss>wood-block printing</gloss>
+<gloss>wood engraving</gloss>

would that keep the "wooden board" meaning? (separated from the "wood-block printing / wood engraving")
the context I've encountered 木板 in was in a japanese game, in the description of a wooden shield made of wooden boards. But I'm aware games are not much of a reference. Sorry I can't contribute anything more to this, the matter is too confusing for me :\

Unidic: 木板/きいた
GG5: もくばん - 【製本】 a wooden board.
実用: きいた・もくはん - 木の板。印刷を行うために字や絵を彫った板は「木版」（もくはん）と表記する。
日本国語大辞典: もく‐はん【木版・木板】 - 木の板に文字・図画などを彫刻した印刷用の版。また、それを用いて印刷したもの
Koj, Daijr/s only have 木版/もくはん - no 木板.
GG5 and other JEs have 木版/もくはん - wood engraving; woodblock printing, etc.
木版	158370	90.6% <- entry 1641990 - "wood-block printing; wood engraving"
木板	16368	9.4%

So:
 - we have three readings in play: もくはん, きいた, もくばん (and maybe もくいた)
 - we have the possibility of merging 木版 and 木板 (as in Nikkoku)
I'm inclined to go with a merger, treating 木版 as the main form and 木板 minor one.

@@ -8 +8 @@
-<reb>もくいた</reb>
+<reb>もくはん</reb>

https://so-kai-app.sakura.ne.jp/blog/2767/2017/10/06/
https://www.weblio.jp/content/木板
https://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q13176566453

I'm doubting the reading given on this entry. The first reference link in the section regarding the もくいた reading says "間違った読み方である可能性が高いです" (because it mix on/kun readings), the second link doesn't even show this reading as a possibility, but it has きいた and もくはん. The third link shows a screenshot from meikyou in which there is the reading もくはん meaning wooden board, but in daijiten the only meaning given is "木の板に文字・図画などを彫刻した印刷用の版。" So I'm not sure on who's right here, but at the very least, the reading もくいた doesn't seem supported by anyone.