The reason why you need to. Leave is to stamp out and to stamp in with the proper stamp. So you can just come back within 5 min and should have no problems.
The difference is that while on visa exempt, they may deem that your movement is trying to stay in Thailand long term without a proper visa and they can deny entry. While having a proper DT will allow you to say that you are allowed to come and go as you please as long as the visa is live and they should not deny entry.
Better to check with immigrstions but I am assuming that you will need to change visas because they will be your legitimate reason for long stay. Some companies will do the application for a work visa and it will be pegged to the company while some may insist that the employee does all the process by themselves. But in most cases that I know, even if you have approval and a new visa from within the country, you will still need to do a border bounce to stamp out of the old visa and in with the new.
If I am not mistaken, if you have a proper visa for long term stay and need to just leave Thailand at the end of each 180 day stay limit, you should mot face any issues coming back in. Just make sure all your stamps are in place, the original visa issued is in your phone or a print out is on hand, then should mot have any issues. It is not like the visa runs of the old days where you try to come back with a new visa exempt stamp. You can stay for the length of your visa but it has to be up to 180 days each time.
If you are a business owner, you can try to use your company to apply for her a digital nomad, work from any where type of visa. Whereby she works in Thailand using online or Internet work, show that she has a steady income from overseas.
To be frank, different embassies in different countries have different requirements so maybe try in some other country. However, another issue may be that income derived from investments may not be too useful to the embassy because even if it shows a monthly profit and you do withdraw it, it may not be considered a stable income.
You wi usually be allowed one extension before alarm bells at immigrations start to ring. It is best to go before your current visa runs out and make the application. Whether you are rejected and asked to leave or not again depends on the officer and or your entry departure history. There is no such thing as legally in any country if you are using tourist visa to stay long term. There are proper long term visas for every situation and some do get away with extending and going in and out and so on. But being allowed to continue doing so whether it is by extending in country or going out and coming back is at the discretion of the officer you face. They can and do have the authority to question and then deny any further extensions or entry if they so deem.
Since you were pulled aside, it will only be a matter of time before a denial comes. Because a tourist visa is what it means. Saying that you have a girlfriend will only be an accepted excuse before one unhappy officer decides that you cannot go in.
My suggestion is to try and get a longer term visa as soon as you can.