Not a plumber but 3 observations:
1) I apologize if this is obvious to you. Make sure when you say "horizontal" you mean 1/4"/foot slope for a horizontal run. No drain line should be truly level.

2) I agree with concern for vertical drop at kitchen sink. Dangerous if unvented. Horizontal (std slope) is also problematic. Horizontal run is too long before reach wall to not be vented. Possible solution: In sink cabinet, if there is room, split off ventline after trap running up then 180 degree U-turn going down(I am assuming cabinet is larger than sink since this must, of necessity, go above height of sink bottom--front, back or one side of sink). Peak should be above sink drain. This new ventline can go under floor, then run with std slope to connect to vent stack. This vent line must stay above main sewer line at all points. This would allow you to run drain straight down. Someone looking under the sink will see a long upside down U with the sink drain tapping into it in the middle of one side of the U and nothing on the other side. Strange looking, but it works.

3) Make sure vent terminates above roof line and away from any wall vents, windows etc.

First off, Totally disregard paragraph 2 above...all the information presented in that paragraph is not only wrong, it is expressly prohibited by code.

Now, in regards to your statement that you are not subject to code, that also is no correct. All 50 states have adopted a plumbing code and where your local municipality or county does not have a local code, the state code applies, although in many regions they don't require permits and inspections so many homeowners are left thinking there is no code requirements. In Ohio one can buy some land outsie the municipal district and build a house and the only permit and inspection you will encounter is for the septic tank & leech field; however, The lack of code enforcement by the local governing authority does not mean there is no code enforcement.

Since the great housing market crash the Federal Government has seriously tightened up on the banks in regards to the types of mortgages they can write.As a consequence the banks have had to really sharpen their pencils to keep their heads above water. Many banks have now hired their own code inspectors and they require an inspection before they will write a mortgage. In addition, many Insurance companies in those regions also have their own inspectors and they will not write or renew a homeowners policy on a structure with major code violations.

Now having said all of that,,,,,,

I have reviewed your plan and for the most part it it fine, but it would still require a bit of tweeking here and there. Actually it can be done much simpler but before I could give you the layout I need a bit of additional information...

1.I need to know which code is in effect in your area...If you don't know, tell me which state your in and I will look it up.

2.Is that tub a clawfoot tub or a skirted tub that will be mounted directly on the floor?