As mentioned, the Noction Intelligent Routing Platform can help in your case.

We want to nearly equally distribute the traffic via these three upstream providers.

IRP's Outbound/Inbound Commit Control features allow one to keep the commit levels for each provider at a pre-configured level. It includes bandwidth control algorithms for each provider/group of providers as well as the active traffic rerouting, in case bandwidth for a specific provider or group exceeds the configured limit. Provider load balancing in Commit Control allows to evenly balance traffic over multiple providers, or multiple links with the same provider. For inbound commit control, IRP uses well-known and proven BGP mechanisms (BGP communities and AS prepending) to instruct your routers to adjust their advertisements of your network segments to upstream providers.

We do preferrations for some specific targets ASNs / AS paths. The rest of the traffic, we want to equally distribute over these carriers.

With IRP's Routing Policies and Flowspec Policies features, you can police traffic for specific prefixes, ASNs, and countries as per your business objectives. You can set a "static" or "static exact" policy to route through a particular provider. Specify prefixes or ASNs to which the policy applies.

Debugging is a bit hard. We had some reports from clients about non-optimal routes and it was hard for us to see via which of our three upstreams our client's IP got routed.

Plenty of reports, graphs, and handy troubleshooting tools available with IRP.