Well I believe that you can make solution A working with a little bit of coding (I'm not sure if you don't mind coding, but we are on StackOverflow, so I think you should consider that).
First of all the design depends on the simple question - should this Request be shared with multiple teams, or only single team? Single team is simple - just add a lookup on the Request, that will point to a Team. When this team is filled in (I'm assuming that choice of this team is done somehow automatically, but it does not matter as in any scenario you would have to choose the team anyway somehow), you run a simple plugin that shares the record for this team. Sharing using SDK is really simple, just use the GrantAccessRequest:
var grantAccessRequest = new GrantAccessRequest
{
PrincipalAccess = new PrincipalAccess
{
AccessMask = AccessRights.ReadAccess | AccessRights.WriteAccess,
Principal = teamEntityReference
},
Target = requestReference
};
So on the form of the request you will keep the owner of the Request and will have a lookup pointing to a Team that is handling this request. Of course you can further pimp it up by for example un-sharing when the request is accepted or declined or the lookup on the request is changed etc. That would keep the POA table more happy as sharing huge amount of records can lead to fast grow of that table, so it's important to unshare records if sharing no longer needed.
If you want to share to multiple teams, you can still create a N:N relationship between your Request and Team and simply share your Request in a plugin on Associate message between Request and Team (this was a standard option before Access Teams were introduced for the users, remains still the only option for teams). This relationship can be show as a subgrid on Request form (it would look like an access team subgrid).
Of course to prevent users from Sharing the Request record on their own (in that case you will not have the Team in your lookup/subgrid) they should not have Sharing privilege. The plugin should do the sharing in admin context.
UPDATE:
As for the POA considerations from the comments: both solutions will make your POA grow, because for both solutions you will have to share the Request either with the team or with the user. If you will use access team you will still have one POA entry for each Request (so 100K entries per year). I believe that the most important thing here is what happens with the Request when it ends it's lifecycle. If it does not have to be visible to the Team, after it was accepted/rejected then you should simply have a mechanism (plugin or some custom app running on some timely manner) that would unshare all the Requests that no longer require sharing, keeping your POA table in reasonable size.
There is another way of handling your scenario that would not require that much sharing/unsharing logic. You can create a "Request Acceptation" entity in 1:N parental relationship with Request. Because it's parental relationship, user owning Request will see all the "Request Acceptation" and "Request Acceptation" will be owned by proper Team (so only this team will have access). Of course I don't know anything about the business logic, but I assume that "Request Acceptation" can contain only the information relevant to the Team which can be copied in a plugin or workflow.
UPDATE2: As I just saw that you cannot unshare the record at a later stage. But I'm assuming that at some point of time Request is done/accepted/finished/rejected or whatever. If at this point both Teams and User should have access to this Request, then maybe it's a good thing to create some kind of separate entity "Archived Requests", that would not be shared, simply cloned for all the principals that are interested in seeing this information and deleting original Request. There are many variations of this idea, I hope that you get it and can adapt it accordingly to your scenario