The more I think about it, the more I like jump beacons, and I think they would be reasonably straightforward to implement for this beta.
These are great thoughts--thank you!
The easiest way to implement beacons is to check for them only at the time that a destination is set. If the destination is in range of a (friendly) beacon, then it works; otherwise, the player gets an error message. It doesn't matter where the jumpfleet is currently--only where it's trying to go. Thus, we can answer your questions:
Mixed fleets: Jumpships + starships move at starship speed as always. They have no restrictions on destinations. If you have a mixed fleet outside of beacon range and deploy jumpships, the jumpship fleet can only be targeted to points inside beacon range (but it moves at jump speed, even through non-beacon territory). NOTE: Explorers are exempt from needing beacons, so we also have to deal with mixed jumpships + explorer fleets (which move as jumpships do).
Captured beacons: If a jumpship is in transit to some point inside a beacon range and the beacon is captured, the jumpship still moves. It can be re-targeted at any time, but only to points inside beacon range. If there are no beacons left, the jumpships cannot move (but the capital is probably always a jump beacon).
Passing through non-beacon space: In this proposal, yes, jumpships have no problem passing through non-beacon space. They don't even need a beacon at the origin point--only the destination (and only when the destination is set).
Beacon activation time: I think it is OK, for a first pass, if jumpship beacons are immediately activated, as soon as a world is designated. This feature is meant to minimize surprise attacks on a distant empire. But once you've conquered a world with slow ships, then jumpships can come in. If this ends up being too overpowered, we can implement activation times.
Beacon details: I think in the first version beacons are just intrinsic to certain designations. Capitals, jumpship yards, sector capitals for the Fire & Movement doctrine, and maybe citadels. The range should probably be fixed at 250 light-years (same as administrative range) but we can change this later as needed. If we allow other designations to get beacons, then I think they should consume labor. [In practice, though, I'm not sure this will be necessary.]
Beacon construction: At some point we'll be able to build space stations in deep space; those will have designations just like planets (though a different set of them). I can imagine one designation will be the equivalent of a jumpship base, which again would come with a beacon. Perhaps there could be stand-alone beacon constructions too--not sure. In either case, they would behave very much like worlds (though with smaller populations) and would get defenses, industry, etc.
Warp transports: Yes, we need to introduce warp transports. Technically, you can use jumptransports in a warp fleet, so I don't think there is pressing need, but we will introduce warp transports. Not sure if they will be built by regular starship yards or if they require a new designation.
Let me know what you all think of this proposal. I think I can at least implement the core concept of beacons in this beta. Other things like constructions and warp transports would wait until a future beta.