There is a free on-line version of Photoshop called "Gimp." Warning - I tried it once, before I tried PS, and was wildly confused. Finally, I just got Adobe's Creative Cloud subscription, with LR and PS. I suspect that you will need PS to keep the DPI up to 300, where you want it. The on-line apps may not get you where you want to be. Maybe someone wise person on this site has additional advice? If push comes to shove, you might be able to find a college or high school student who can generate this in PS for a fairly nominal sum. One last thought - consult YouTube? It is a clever and creative logo, so good luck creating it!
If you have the name of the font that you want to use and a drop box you can upload it to there and I can add the text to it if you like. Might not be able to do it this week but for sure early next week. Uploading to a large file transfer site should not lower the dpi of the image. Feel free to email me if you like.... christinesmeath@ymail.com