We have an ASA running eigrp in the inside interface, and there are a few other layer 3 switches (6500, 3750G) in the same subnet as the inside interface of the ASA, all running EIGRP, with authentication. On the ASA, there is a default route pointing to the ISP router, and I have redistribute this default route into EIGRP by using 'redistribute static route-map' under the eigrp process.
The problem is the ASA can learn all routes from the 6500 and 3750G, the 3750G can learn all routes from ASA and 6500 including the default route from the ASA, the 6500 can learn all routes from ASA and 3750G, but not the default route from the ASA.
That is a wonderful observation! I am not sure I would have spotted it. Good work! Certainly, individual EIGRP routers in an EIGRP domain should have unique Router IDs so let's start by making sure that they indeed have it unique.
The EIGRP Router ID is selected precisely in the same way as in OSPF - first the highest IP among loopbacks, and if no loopbacks are present, the highest IP among active interfaces. It can also be set manually in the EIGRP configuration using the command eigrp router-id A.B.C.D.
To answer your questions:
1.) Rebooting will make EIGRP reinitialize its Router ID. Therefore it will help if the loopback IP addresses are unique among your routers.
2.) Yes, you can. The EIGRP will again reinitialize its Router ID when configured anew.
3.) I have described it a few lines before - first the command "eigrp router-id" is used. If that is not present, then the highest IP among loopbacks, and if they are not present or active, the highest IP among active interfaces.
4.) Yes, I think that the redistribution is fine.
The easiest way now is probably to just use the command "eigrp router-id" to force the ID to a unique value and then see what happens.