You will need to show self employment income (W2 salaried or draws ~ it doesn't matter) for atleast 2 years.
So ... 2015 and 2016 ... Outside of a local CU or local bank, I just don't see you getting around the 2 year minimum.
...the only thing I'd add to the prior poster is that 60k in savings going for 150k home with your scores is going to be a very positive factor in your mortgage search ...plus you have 3 years of stable W2 wage history in your current IRS files
...I'd want to see your mortgage scores before saying anything else ...they can vary +/- 50 points or more from your 08 scores ...spend the $40 to pull your 3B and lets see if the mortgage scores hold up ...if they do, I'd think you'll have a good chance of finding a lender willing to give you a mortgage even with your 4mt problem ...hth
I think self-employed for you is a misnomer...
ETA: I was wrong, mea culpa.
Hey, thanks so much for the reply. On the chargeoffs, how would paying those even work? Should I try to contact the lender now and do that? Would it drop the item off my report? And how long for the other negatives to drop? Anything else I can do to make sure this isn't an issue?
My mortgage scores are 768/769/790.
What, hypothetically, is the low range of "great scores" where I wouldn't have an issue on that front? 700? 720? etc.
Re: self-employment, we have plenty of cash and revenue so barring some catastrophe, I should still be gainfully employed 
It's a bit odd since the business has been around since 2013, but was spun out of where I previously was employed. So on paper, it's new, but it has a few years of history. Complicated, I know.
Thanks again for the response!
@Anonymous wrote:Hey, thanks so much for the reply. On the chargeoffs, how would paying those even work? Should I try to contact the lender now and do that? Would it drop the item off my report? And how long for the other negatives to drop? Anything else I can do to make sure this isn't an issue?
My mortgage scores are 768/769/790.
What, hypothetically, is the low range of "great scores" where I wouldn't have an issue on that front? 700? 720? etc.
Re: self-employment, we have plenty of cash and revenue so barring some catastrophe, I should still be gainfully employed
Thanks again for the response!
Paying off a charge-off won't drop the item on your report, but it will reduce it to a zero balance which your mortgage lender will most likely want to see (again this is an area where each lender varies, the ones I have seen require them to be PIF). Check with the creditor to see if they would do a PFD - Pay For Delete, as this will be most beneficial for your score.
Honestly score doesn't make a big difference in qualification as much as people think it does. Anything 740+ is generally enough to get the best pricing, and most lenders employ a risk-based pricing model to price anything between that and usually 620. So you do start to see pricing hits at 730, 720 depending on the other factors (for example, an LTV (Loan To Value ratio) below 60% usually wipes out a lot of pricing hits for FICO) Basically the lender tacks on additional points the riskier the loan gets from a FICO/LTV standpoint, and then once you get below 620 most won't do the loan at all. You shouldn't have anything to worry about with those scores though.
The lates are not a big deal as long as your score is good (which it is) and you get AU (Automated Underwriting) approval which they'll be able to tell you right away. I don't expect it being an issue since they're from 2012. Beyond that there usually isn't a guideline on lates. Sometimes if you're taking out mortgage insurance (+80% LTV) the MI company will have a guideline overlay about how many lates you can have in the past XX months to qualify, but yours are too old to fall under that.
I'm sorry but as an ex-underwriter I have to disagree with the previous poster about just telling your LO that you're not self employed. Traditional lender definition of self-employment is if you own 25% or more of the business or if you engage in contract work (1099/Sch C). This is the guideline used by the two major GSEs (Fannie/Freddie). It has nothing to do with how you pay yourself and in fact paying yourself via W-2 while owning the business is quite common. The app will specifically ask if you're self-employed (which you are) as will your LO, so not telling them this would amount to misrepresentation.
In terms of business age, lenders are going to look at how long the business has been on your returns for, and calc the income by looking at not only what you pay yourself, but by doing what's called a "cash flow analysis" based on the business returns. The major GSEs only permit this to be calculated off of validated federal tax returns, and with a 1 or mostly 2 year history to prove over time that the income from the business is stable and likely to continue. Some local credit unions might go out on a limb for you if you're lucky, but in general any normal conventional lender that sells to a GSE (i.e. virtually all of them) is going to have their hands tied on this one with only 4 months SE history. I would not sink any money into it right now though as there's a good chance it won't pan out this year.
https://www.fanniemae.com/content/guide/selling/b3/3.2/01.html
...I think that's definitive as far as FM loans go ...which is a very long way ...the pp is correct as far as he goes ...but he only goes to his own experience
...if your Fico mortgage scores hold above 740, I still believe that you will find a "portfolio" lender more than willing to work with you ...there are a number of lenders who will hold your mortgage themselves and not sell it into the FM aftermarket ...and thus are able to and will consider your actual income history as well as the business's in a positive light ...you will likely pay more in rates but then thats also true if you wait another 8 mts because rates appear likely to rise ...are rising.
...I'd get those mortgage scores ...if the middle score is 740+, I'd get on the phone with your realtor asking for recommendations for portfolio lenders they have worked with successfully ...any large realty has done this and many lesser ones, its not a small market.
...you'll get a lot of feedback here ...all of it is colored by the personal experience and knowledge of those providing it ...that implies limits ...including my own ...but it also implies there are solutions to most mortgage problems ...which is why this forum exists ...to find a way to "yes" if such indeed exists however difficult the route may be ...hth