I was reviewing my Anki cards and it said that 減少 and 増加 are antonyms. Now, for extra practice, I try to give at least one kunyomi reading to each kanji. Then it occured to me that ふえる and へる sounded similar. This question may sound crazy and naive, but could they be etymologically related, considering that some words spelled with え now used to be spelled with へ?
In Japanese, phonetic equivalence is generally a very poor predictor of common etymology. Japanese is well known as having a preponderance of homophones, mostly due to the accretion of possible readings for each kanji which has developed over the centuries. But even among wago (和語), verbs ending in 'eru' are extremely common. Still, it is always worth researching individual cases.
A search of the words on Daijirin doesn't reveal evidence of a common etymology, at least from the definitions here and here. I also checked Kojien (広辞苑第六版) - it lists 減る as appearing in the 'Genpei Sesuiki', an extended version of the Heike Monogatari (approximately 12th century). According to Daijirin, 減る also appears in the Koyo Gunkan (17th century), so presumably, the word was in regular use during the interim period. I couldn't find any contemporaneous examples of 増える, checking in the same Kojien edition and Shinmeikai (新明解国語辞典 第五版). That doesn't mean it wasn't in regular use, of course. But without solid examples of usage that provide context for the words, I can't find any evidence to support your hypothesis of a common etymology.
Nonetheless, it's an interesting hypothesis in light of the phonetic changes you mention. However, I think we need more details on how those specific words might have undergone change before we draw any solid conclusions about their derivations.