While you're getting a lot of good analysis about what has happened to you so far, you specifically asked,
How do I interact with this employer moving forward?
Since you seem to have some legitimate concerns (compensation, workload, risk of working for a small employer) and your employer also seems to be concerned (their tiny company is at risk of folding if you leave) it makes sense to have an explicit conversation about these concerns, instead of being indirect about it.
While it's nice to get a raise now, it's even nicer to have a roadmap for how your concerns will be addressed in the future. So, before you talk to your employer, it makes sense to come up with a list of what your goals and concerns are.
Once you have a list, you can set up some time with your boss to discuss. The key to this conversation is to be specific about your concerns. Often, the awkwardness you and your boss experienced is because people naturally tend to be vague in conversations like this. Your boss saying we really appreciate all your hard work doesn't really change anything, it's not actionable, and it probably doesn't directly reference anything that you care about.
If you want the relationship to change, take some initiative. Put some specific items on the table, and ask your boss to specifically respond. Based on the content of your question, you might try things like,
I'm worried because people have left recently, and that leaves me with a lot of extra work. I don't think I will be effective if I'm constantly working a lot of overtime, and I don't think the company is in a good position. Can you talk to me about your plans for properly handling this workload in the future?
I'm unhappy because I've made contributions X, Y, and Z recently, but my pay hasn't reflected the value I'm bringing to the table. I don't want to sound like I'm holding you hostage, but I need A, B, and C to change in order for me to feel comfortable staying at this job. Can we work together on a plan to change those things?
Asking for - and even getting - a raise is often not effective in actually solving root problems that are making an employee unhappy at work. You are a perfect example of this - you asked for more money, and you actually got it but you are still so unhappy that you're thinking about leaving. If the thing that bothered you was the way they handled the process about deciding on your raise, you could bring that up as an issue:
Although I'm grateful at receiving my raise, I felt like we could probably both agree that the process was really awkward and uncomfortable. I'd like to avoid that in the future. Do you think we could talk through what your decision process is for raises? Can we make plans for a regular annual review and come up with some standard way on determining an annual salary increase?
The key in all these suggestions is that you are being specific in describing your problem, and you're giving your employer an opportunity to address your actual problem (instead of just awkwardly throwing money at you). You're putting the ball in their court. They can respond, or not. And you can decide if you're happy with the response. And, of course, you can still choose to leave if you're unhappy, but even if you choose to leave, you've at least given them the benefit of the doubt and you've made it clear to everyone that you are not a good fit for their company.
And, as a follow up, any time you're considering leaving a job, you want to make sure you're not going to just jump into the same problem all over again with your new employer. Even if you choose not to talk to your current employer about your issues, it makes sense to spend some time thinking (or even writing) about specifically what made you unhappy. Think through your whole relationship with this employer and see if you can determine the root causes for your unhappiness. Then, consider how you can use that knowledge to evaluate future potential employers.
You may decide that you like working for a larger employer, or one with a certain level of structure. Or, an employer with a lot of depth on a given team, versus a small team. Or, you may decide you need an employer that has a formal, annual evaluation process that is tied to decisions about increases, since that sort of system will remove the ambiguity around raises. Whatever you decide, come up with a list of questions you can ask in interviews, so you can make sure you know whether a given employer fits you needs. This way, you can avoid the disaster of repeatedly jumping ship because you're never happy for the same reasons over and over again.