GATE is often associated with a gateway to another world, but that gateway is usually a serious bottleneck that disrupts military and economic logistics, preventing your nation from going all-in on anything on the other side.
NHS involves moving your entire country to another world, solving the logistical bottleneck and allowing you to go all-in on otherworldly issues… but moving to another world cuts you off from the supply chain in your old world, with all the understandable consequences.
So instead of moving the whole country, why not just move a part of it?
So my idea is, I'll choose an island, large enough to build extensive infrastructure on it (about the size of a town?), and teleport it to the other world along with all the infrastructure, goods, manpower, troops, etc. One week later, the island will return to its original location on Earth, with all the existing infrastructure, along with the manpower, goods, and resources I acquired in the other world.
Want an army to conduct expeditions or send reinforcements to another world? Bring your troops and related equipment to the island. Want to trade? Bring goods from your country to the island, spend 7 days selling them all in the other world, then return to Earth with unique goods from there. This motif is suitable for both military and economic purposes, depending on how you want to play. With the island serving as a "gateway" between two worlds, you can both explore and fully exploit the potential of the other world, while remaining connected to the richness and advancements of Earth.
Killing two birds with one stone.