It sounds like your group is suffering from analysis paralysis. It's more common in games like Shadowrun that focus on preparation for big jobs, but it can certainly happen in D&D.
As a player, I wouldn't try and get authority. I've not seen a successful case of a "party leader" actually leading, and players often get annoyed by a character moving off on their own.
Your best bet as a player is to (paradoxically) speak to the other players OOC. Letting them know that the discussion seems to be taking a while and maybe even voting on a course of action might help. If the feeling of "metagaming" bugs you, consider the fact that your characters are highly-trained adventurers who have become good at working together; your OOC decisionmaking just simulates their IC teamwork.
As a GM, you have a much better chance of improving things. I often have players hyperanalyze decisions, and as the GM you can guide the decisionmaking. There are a number of things a GM can do to break up the decision stalemate:
- Provide an explicit set of choices without actually railroading: "It seems like you can do X, Y, or Z, unless you can think of another approach." Usually they'll take one of your choices.
- Resummarize their discussion. Often discussions can go in circles, and this can be broken up by quickly summing up the arguments they've made and the options they've considered.
- Tell them what their characters would know. You can have them make Wisdom or Intelligence checks, or just tell them outright. Their characters' world knowledge can tell them when a course of action is particularly foolhardy or ignorant.
- Limit their ability to have discussions in some circumstances. If their characters have time pressure or are in a situation that precludes conversation, remind them of this or let them know that anything they say can be overheard.
And don't be afraid to review parts of the rules that they don't know! I actually think it's unrealistic to expect all players to read the whole rulebook, but they should certainly know the rules that pertain to their character.
As a postscript: I'm not sure if you're considering this, but I recommend against keeping your PC as part of the group while you're GM, and especially recommend against putting them in charge. It's best to keep the focus on the other players' characters.