OK.

I don't think sense 2 is a counter; it's a unit of measurement like リットル and キログラム, 
which we don't say are counters.

@@ -22 +21,0 @@
-<pos>&ctr;</pos>

gg5 (sense 3)
daijr 4: 学校などで、授業の単位として設けた、一定の長さの時。時限。助数詞的にも用いる。 「国語の－」 「三－目」
daijs 4: 授業や勤務など、ある一定の区切られた長さの時。「算数の時間」「勤務時間」

I think sense 2 is also a counter and that daij pretty clearly mark it as such. Daijs: 3 時の長さを数える単位。時(じ)。「1時間は60分である」
Daijr: 3 時間の単位。3600秒。助数詞的にも用いる。 「飛行機だと二－で行ける」
It could also be a separate sense (like in daij) but I don't know what we'd accomplish by that.

@@ -21,0 +22 @@
+<pos>&ctr;</pos>
@@ -23,0 +25,6 @@
+<sense>
+<pos>&n;</pos>
+<gloss>period</gloss>
+<gloss>class</gloss>
+<gloss>lesson</gloss>
+</sense>

gg5

not a counter. a "counter" is something (usu. one character?) that is not a word on its own but gets suffixed to a number to make a word.  this is a word that means "hour"

none of my sources has this as anything other than a noun

@@ -21,2 +21,2 @@
-<pos>&ctr;</pos>
-<gloss>hours (period of)</gloss>
+<pos>&n;</pos>
+<gloss>hour</gloss>