How do I schedule work on the ThreadPool without causing thread starvation

Question

I am consuming messages from a queue, and want to invoke a message handler such that I am processing messages as fast as possible. The message handler is asynchronous, but also does some CPU work.

I have considered the following approaches:

1. On each message call Task.Run

    foreach (var workItem in GetWorkItemsFromQueue())
    {
        Task.Run(workItem);
    }

2. Same as 1, but try and not exhaust the ThreadPool

    foreach (var workItem in GetWorkItemsFromQueue())
    {
        while (ThreadPool.PendingWorkItemCount > 10)
        {
            await Task.Delay(1);
        }
        Task.Run(workItem);
    }

3. Use Parallel.ForEachAsync with 'unbounded' concurrency. Initially i was using -1 as per the docs, but changed this to int.MaxValue based on comments below

    var options = new ParallelOptions
    {
        MaxDegreeOfParallelism = int.MaxValue
    };
    await Parallel.ForEachAsync(GetWorkItemsFromQueue(), options, async (workItem, token) =>
    {
        await workItem();
    });

4. Same as above, but with the default MaxDegreeOfParallelism (i.e. Environment.ProcessorCount)

    await Parallel.ForEachAsync(GetWorkItemsFromQueue(), async (workItem, token) =>
    {
        await workItem();
    });

5. Use LongRunning Threads. Admittedly this isn't actually using the ThreadPool

    foreach (var workItem in GetWorkItemsFromQueue())
    {
        Task.Factory.StartNew(() => workItem().GetAwaiter().GetResult(), 
            TaskCreationOptions.LongRunning | TaskCreationOptions.PreferFairness | TaskCreationOptions.DenyChildAttach);
    }
    return Task.CompletedTask;

The most obvious approach would seem to be simply calling Task.Run(...) but with this approach I notice the ThreadPool.PendingWorkItemCount quickly growing.

Ideally I would like the ThreadPool queue to act like a BlockingCollection of capacity 1, which is what example 2 is trying to achieve.

Ultimately I feel like this must be a solved problem, but I'm struggling to find the solution, so I'm hoping someone can point me in the right direction.