pwill:
276B is a provision allowing, in exceptional circumstances, people who would not otherwise qualify for indefinite leave to remain to get it. It is for long-term illegal immigrants, for example. The important distinction is that it presupposes that your 10 or 14 year period in the UK is contiguous with the time of your application - i.e. you apply from the UK and the "look back" is 10 or 14 years from the date of application. In your case, they would "look back" and you would be out of the country for the last 4 years. I think you would be disqualified on that basis.
Your situation is really a different one - you already HAD indefinite leave, but you were out of the country too long. The way I see it, the ONLY question in your case is whether sec. 19 applies and whether they will exercise discretion in your favour.
Sec. 19 is discretionary. I think the factor that you may be wanting to sponsor someone at the same time could weigh against you. On the other hand, you may be ok, but it could be a hassle. Like I said originally, I think this is a gray area question. Talk to a solicitor.
Note that one poster's information dealt with a situation where the American spouse had a British wife and they gave him the returning resident stamp despite his being in the US for more than 2 years. This is not really comparable, because having a British wife basically means he could have come in with a spousal visa anyway. So they just gave it to him. In your case, on the other hand, it looks like they have a chance to deny you. In addition, you also want to sponsor someone else for immigration. So they would get to deny two at once!
As you appear to be an Irish citizen anyway, if I were you I would just push hard to get the Irish passport. I don't really understand why it should take 6 months, because according to the information on the Irish embassy website, if one of your parents was born in the Republic of Ireland, and you have your and their long form birth certificate as well as their marriage certificate to prove it, your Irish citizenship is automatic (from birth). It does not require the "foreign register of births" rigamarole. You are entitled to the passport, full stop. Can you go to the Republic of Ireland, get your documents together, and apply there in person for the passport? In London UK passports has a fast track passport service whereby you book an appointment, go with your documents, and your passport is ready for collection the next day. Ask a solicitor in Ireland whether it can't be done more quickly. There are usually a few ways around bureaucratic hurdles.
Is it the Irish consulate in the US that says it will take 6 months?