Hi Alex,

First welcome to the forum...

As for size recommendations, I don't really give those out anymore for liability reasons via forums and/or only having basic information about a project. There is way too many complexities to a timber frame (unknown load parameters, wood species, grade, Timber Framer's experience, future load parameters not shared for a floor diaphragm, etc...) to make such advice viable or "good practice" professionally within this craft...

What help I can offer is that even professionals (myself included) always have our projects (at minimum) checked by qualified PE that not only have the requisite credentials, but timber framing experience as well. I have been working with (and friends of) the same firm for over 30 years now (Fire Tower Engineered Timbers) and could not recommend them more highly for any project, commercial or simple cabin structure or play house. IF!!!...I don't use an Engineer on a project, that is by the clients choice and I still won't go outside of scope for timber sizes of those found in previous projects that have already been approved and/or I require a "hold harmless" contract with those clients.

As for your project, it reads as exciting, but the size (no wood species or grade was offered?) seems out of proportion as "4x stock" is not often found as major carrying beams and usually relegated to joist (4x6, 4x8, 4x4, or their metric equivalent) for most timber frames in that size range you have shared. "Tidewater Capes," as one example, had these size timbers (aka narrow and deep) but each frame design in that style is specific to a given project and/or regional vernacular style and is out of context for a "first project," (in my opinion) for a novice Timberwright. There are recommendations and charts in several of the timber framing books, and on line, yet again, these are "basic" in nature or follow only a set design that has already been engineered.

From an aesthetic perspective, I would suggest either the timbers being closer together with a heavier T&G structural floor diaphragm, or wider "live edge" timbers that are at minimum a 8" deep and no further apart than 24" on center, though other configuration are possible depending on wood species, grade and loads...

Good Luck and would love to see pictures shared here when you get this all figured out. Others here may be of more help than I have been with their recommendations...