Can someone help me identify the base font used in the Persona Q. I tried to usual machine identifers such as fonts.com and likefont.com, but no luck. I know it may me hard to identify since the logo has alot of intentional text warping, but help on this would be appreciated.
What is presented is likely a one-off hand-made creation, especially as the upper and lower portions are merged in the manner displayed. One could consider that the overall style could be called "60s hippie" and a search using "60s hippie font" presents a number of similar images associated with respective typefaces. You will not find an exact match, but using similar search terms, may find something suited to your objective.
From one of many links: https://www.pinterest.com/pin/18647785941832113/
I guess you are not going to make a replica of the shown logo, but to make your own logo in somehow resembling style. If that's right then stop searching the right curvy font. Instead learn to mangle outlined (=converted to paths) letters in a vector drawing program. It works well after one understands how the most basic path editing tools work.
Of course, one must also have a consistent idea of the wanted result. All tinkering is useless without a goal. Many of us make coarse sketches with a pen on paper, because then the idea is dominant. Doodling with a computer easily prevents it to get a shape worth to be called an idea, one gets only an aimless mixture of effects.
The sketch can well be as coarse as one's drawing skill limits. Nothing prevents refining the idea with the computer if there's something to be refined.
Here are few tricks in Inkscape which can be useful. The shown texts are all made of simple bold font. The letters are converted to separate paths (Path > Object to path, Object > Ungroup)
At first: In every case there's no need to warp adjacent letters to the same form to get a clean border:
P is moved to top and got a background colored (=white) stroke. No hole is made to the left edge of E.
The the letters are often quite complex paths (=much nodes) because they must obey exactly the glyph forms drawn by the type artist. One can simply delete as many nodes as needed to get a simple enough path. In addition one can push and pull with the node tool the edges, nodes and node handles. Some nodes can be converted to corners, some others to smooth ones and some also to symmetric, if needed. Symmetric node makes no apparent angle, the edge turns smoothly.
The next image has the original S and what's got by deleting most of the nodes and doing a few pushes and pulls with the node tool:
Here's another example. The original E is simple because it has only straight lines. In the right there's an edited version made by only moving some nodes and pushing and pulling shape edges with the node tool:
Then there's a common outline which seems to have a certain distance to the letters. One can constructed by using path offset effect. The holes must be filled by inserting patches.
In the next image I have 3 letters converted to paths and ungrouped to separate paths. That's because path effects do not work right with groups:
In the next image I combined the three paths to one by applying Path > Combine. The combination is duplicated and one of the copies has got blue fill color:
Combined path can be broken apart, but it's not the same thing as a group. Combined paths accept path effects and Boolean operations such as unite or intersect.
A way to get nice automatically rounded offset outline is to apply Path > Dynamic offset. It has width adjustment handle for visual trimming. The blue version got it. The original vanishes - that's why I made the duplicate:
Alternatively one can insert path effect "Offset" which has more options for corners, not only rounding.
There's a small hole. It can be covered by inserting a blue rectangle.
In the next image the offset version is sent to back and the black text is moved on it. The selected item is the blue rectangle inserted to fill the hole:
Hopefully here's some ideas to get the job done. Good luck!