Simply don't LIE to the seller!

if your problem is capital and not your DTI. there's really two ways to go about this. 1. simply save. qualifying for a  200k place means you have probably 9-11k saved up for a place including closing costs. so just increase that by 50% and whoop theres a 300k place for you. with some strong saving, you could probably do that in 6-12 months. 2. use gift money from friends and family. you can take these gifts for personal residences.

I simply wanted the ease of moving on a new investment every time I have enough equity in the HELOC.

There may be better opportunities potentially, I don't know your area so can't comment but the fact is that you'll be paying down your mortgage by simply managing the property while enjoying rent & property appreciation with equity being built at no cost to you.Assuming 20% down, your returns will far outweigh putting the cash into the stock market.ie. for simple numbers 100K property that you downpay 20K on.

If they insist simply say they did not meet your qualifications that you set .

I just want to add that retirement accounts are designed to be invested passively, a better use for your Roth IRA money would be to simply be the bank and lend it to another flipper.  

It could simply be priced too high.

So what's the cost of a loan, tied up money in an attempt to save potentially 10-15k over three years.

So assuming we will attempt to get a conventional mortgage, what order should we do things... pre-approval and then HELOC, or vice versa, at the same time (if we went through same bank), or does it not really matter?

A duplex and a home with a secondary suite simply do not compare.