(The idea of) Gaman is taking stopgap measures and getting away, not knowing what else to do, even though you have complaints.
ながもら should be a typo for ながらも, a stiff way of saying "even though". 乗り切る is "to go through (a difficult part)", "to get away (from an undesirable situation)", etc. しょうがなく is "having no other choice", "as a last resort", etc. And let's not overuse "say" to translate という, see this.
Anyway, that article is not something you can trust as a language learner. The article is saying 耐える is a more positive word used with a future prospect, but I don't agree with this explanation. In addition, 耐える has etymologically nothing to do with 多得る; it's just his own wordplay.
The fundamental difference between 耐える and 我慢する is in their usages.
耐える is an intransitive verb used in the form of ～に耐える, and its used with some unwanted stress, situation, attack, desire, etc. When the target is a clearly external one, 耐える is the only choice. The subject of 耐える can be an inanimate object, too.
我慢する is a transitive verb, and it can be used with something you want to do, especially your own desire.
Use 耐える for external things:
- 我々は敵の攻撃に耐えた。 (敵の攻撃 is external and undesirable)
- 困難に耐えた。 ("hard situation" is something clearly external to you)
- この防具はライフルの弾に耐えられる。 (防具 is inanimate)
Use 我慢する for things you want to do/use:
- 食事を我慢する, 食べたいのを我慢する
- シャワーを我慢する, トイレを我慢する
Both can be used when the target is an unwanted internal feeling/desire:
- 眠気に耐える = 眠気を我慢する
- 空腹に耐える = 空腹を我慢する
- 痛みに耐える = 痛みを我慢する
When two are interchangeable, I feel 耐える sounds a little stiffer and more formal.