### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### What happened?

## What happened?

We run wildcard BYOK routes alongside normally priced models:

```yaml model_list: - model_name: claude-opus-4-6 # normal, proxy-keyed, billed litellm_params: model: anthropic/claude-opus-4-6 api_key: os.environ/ANTHROPIC_API_KEY

- model_name: anthropic/* # BYOK: user supplies the key, cost must be 0 litellm_params: model: anthropic/* api_key: os.environ/ANTHROPIC_BYOK_PLACEHOLDER input_cost_per_token: 0 output_cost_per_token: 0 ```

We observed two intertwined billing bugs on v1.87.0 (code paths unchanged on current main as far as we can tell):

### Bug 1 — custom pricing lost when `litellm.model_cost` is replaced

`response_cost` for deployment custom pricing is resolved through `litellm.model_cost[<router_model_id>]`, registered by the router at deployment creation (`Router._create_deployment` / `add_deployment`). But:

- `_check_and_reload_model_cost_map` (and the admin force-reload endpoint) does `litellm.model_cost = get_model_cost_map(url=...…