for a HELOC to fund the construction overruns
This why I opined purchase. In this case I see the HELOC as a const/perm loan. It is for the construction of the dwelling and it would be the permanent financing for that portion of the construction.
A HELOC would not be temporary financing, or if it is then it shouldn't have been processed as a HELOC because that would be structuring a closed-end credit as open-end credit to avoid disclosure requirements.
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The opinions expressed are mine and they are not to be taken as legal advice.