Hey there! I have a BA and MA in History from a public university, and I was accepted to Harvard's HoS PhD program starting Fall 2024! If I can accomplish this then you most definitely have a chance to gain applicable HoS skills.
For more background - I study disability history and completed an MA thesis on this topic in my traditional History MA program. My advisor with a traditional History PhD has moved into disability history within the last few years and was able to provide me with a plethora of feedback, guidance, and readings to do well in the topic. I also had a minor in Political Science on my BA degree, which I used in my application to express my ability to succeed in an interdisciplinary HoS environment.
Do the programs you were accepted into offer cross-course listings with other departments, or certificates in a topic related to your interests? If they are willing to offer this kind of flexibility (which many traditional History programs oft do to increase your skillset) then I don't see this being an issue! Graduate programs are a great place to network, research, and increase your theoretical background, so I think a program might be a better place to improve your credentials than on your own!
I am, of course, just an internet stranger Do what feels best based on your path! I hope my two cents may help ease any anxieties though.