Retry method for generating unique code

In an app, a user can initiate the generation a six-digit alphanumeric code (actually done via Web API). The code needs to be checked against a remote database to ensure it is unique. Other than for diagnostics or logging, the DB table is only used by the Web API and an Azure web job that cleans out expired codes.

In my tests, collisions occurred on average only one in ~24K times with a high of 85K and a low of 170. It is the latter that concerns me. Although the table is emptied of expired codes daily, at some point there will be a collision. Although unlikely, it could happen with very few records in the table.

It is worth noting that because of exterior requirement, the code is limited to six characters from AEFGHJKLPQRSTUWXYZ123456789.

A simplistic solution would be to keep running the generation/check until a unique code is created. In all likelihood, this would only mean 1-2 iterations. But there's no guarantee. And certainly it can't run unfettered.

The next step would be to put a limit - say 5 tries - through a simple loop. This may be enough of a solution. Despite concern that the user would be frustrated if it ultimately fails, if it does there's probably enough wrong with the overall system to ruin the user experience anyway.

I have good exponential backoff code so although this is not a network issue (also a concern), it may help to incorporate it into the retry scheme. In fact, that might be a nice catch-all solution. Given 5 increasing temporal delays in retrying, it would allow both enough chances for the logical code to exceed the chances of a collision and mitigate introducing more stress on network resources.

Any suggestions/observations would be appreciated.

FYI, this is the code used to generate codes:

    /// <summary>
/// Generates a randomized alphanumeric code
/// </summary>
/// <param name="strLength">e.g. 6 chars</param>
/// <param name="charSet">e.g. AEFGHJKLPQRSTUWXYZ123456789</param>
/// <returns>string of the specified length</returns>
public static string GenerateCode(int strLength, string charSet)
{
    var chars = charSet.ToCharArray();
    var data = new byte[1];
    var crypto = new RNGCryptoServiceProvider();
    crypto.GetNonZeroBytes(data);
    data = new byte[strLength];
    crypto.GetNonZeroBytes(data);
    var result = new StringBuilder(strLength);
    foreach (var b in data)
    {
        result.Append(chars[b % (chars.Length)]);
    }
    return result.ToString();
}