This section is meant to investigate, understand and ideally solve issues that come up alongside the building processes.

Double Dome Dipole Tweeters

With dipoles it is possible to retain a usable figure of eight pattern up to ~1.5 KHz...2KHz. Then the rear radiation of the mid driver has started to roll off. It is always the tweeter section that is most problematic because the physical dimensions become large compared to the radiated wavelength. So the logical conclusion is to shorten the effective dipole length and make everthing smaller. The following illustrates the typical behavior of dome tweeters with a minimum baffle in dipole application.
The devices under test were two NE19VTC-04, for DIYers aka NE 200 VC. The dipole length is as small as 110 mm.

Up to ~2.5KHz there is good dipolar behavior. Unfortunately, the first null and partially even the consecutive ones become visible. Latter is the result of the pretty wide dispersion this driver is capable of.
The circular "baffle" is certainly an extreme but a rectangular one would not help enough while keeping the path length short.
The smaller a real source and the wider its radiation is, the closer the pattern follows the mathematical dipole model. In this case this is undesirable because the cosine pattern as such is not usable in speaker application. In practice, it is the balance of directionality and equalization that makes it usable. And “balance” can be taken literally if the radiated wavelength becomes significant.
Between 3KHz and 13KHz the radiation pattern is all over the place.

If the dipole length would be decreased even further than in this example, more controlled directivity is gained but the frequency range where there is dipole cancellation broadens. In turn, this makes it more and more difficult if not impossible to integrate the tweeter into a proper cross over transfer function. Boosting is not an option with those fragile drivers and even a modest attempt has a negative impact upon output capability. So would have equalization with a Linkwitz transform in conjunction with a BW2 HP, making it only an acoustical and not an electrical LR4 transfer function in total.
So in this simple form, dipole tweeters using two domes is a dead end.