How can I strategise IC with the other players when my PC is stupid?

I have a very strong preference for keeping discussions in-character and avoiding out-of-character table talk. The trouble is that my PC is not very smart (an Int 8, Wis 13 half-orc barbarian) but I’m one of the more experienced players at the table.

How can I contribute usefully to strategy discussions we have in-character, while faithfully role-playing a stupid character?

Do I have to just accept that the only way is to make suggestions out-of-game?

The background to this question is that I’ve already run into problems because of the combination of avoiding out-of-character discussion and avoiding suggesting smart things in-character.

As a player I like to overcome the challenges which are presented, so I do want to think about the best way a situation should be handled, in a way that good prevails (I tend to play Chaotic Good alignment) and everybody survives to see another day – barring accidents and bad luck. The other players don’t bother planning on how to tackle challenges, and usually just run into them head-first.

So my character is a simple barbarian and I mainly kept to that role in the party: I smashed things and use brute force, no questions asked. The problem is that I stopped thinking about making intelligent suggestions to the group because my character would never do that. This resulted in two characters dying in an unwinnable fight against an enemy that outnumbered and out-powered us, because the party tried to hack & slash through an adventure that could have been easily won through negotiation and strategising to play two factions off against each other.

I don’t mind things going badly due to crappy rolls, but it haunts me that things went badly because I decided to keep quiet.

Is there a way to get my strategic plans presented to the party through my not-so-smart character, or do I have to just break character and strategise out-of-character? Is there any way to reconcile my two priorities of staying in-character as a role-player, and successfully strategising as a game-player?