There is very little alternative. If you want to talk to a database (any database, not just Oracle) you need a client. This has nothing to do with DOA. This would have been true if you had used the BDE or ADO, in which case you would have had even more installation woes, and for the future, all kinds of potential versioning problems. If you don't want a client, use Java and JDBC (in which case you will have a client, but packaged into your app, and miserable performance to boot).
Allround Automations cannot package or distribute Oracle clients for the simple reason that they don't know what database version you're working with, apart from the fact that it would probably be illegal.
The install is simple enough, but depends a bit on the Oracle version you're using. Seeing the number of users you're talking about, you must have an IT-department capable of doing this. As a matter of fact, I am somewhat surprised that your IT-department has allowed a database into the organization without considering the deployment and maintenance issues involved.
Finally, a few threads back there were some posts concerning bypassing the Oracle client. This is possible, but opens up a whole new set of issues. Security is one of them, but I can think of a lot more.
You could also consider multi-tier solutions. DOA has a neat little 3-tier demo.
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Frans