How to configure AutoMapper 9.0 in IIS hosted WCF application

Question

I want to use AutoMapper 9.0 in a WCF project containing several services that will be hosted in IIS. I've only found one other related SO question but its dealing with a 10 year old version of AutoMapper and is not asking the same question. Its answer is similar to the top hits on Google which suggest using a ServiceBehavior but that doesn't seem applicable when I want multiple services to use the same mapper. The defense rests.

In a web project, you might create a static MapperConfiguration in the Global.asax when the application starts, but WCF doesn't have a Global.asax. It looks like there are a few options for executing initialization code in WCF:

1. Include an AppInitialize() method in the App_Code folder. This will be dynamically compiled at runtime and people have complained that it can have missing reference issues in IIS so I'm not confident AutoMapper or its dependencies will be found once deployed to IIS.
2. Create a custom ServiceHost. This seems like it would execute once when the application starts, but also looks like it ignores the web.config configuration, which I don't want.
3. Use the Configure method per service. This has the same drawback as #2 and also I become concerned with thread safety (as in the ServiceBehavior approach) since two services could try to initialize the MapperConfiguration at once.

I considered just creating a class with a static property that would create a static MapperConfiguration or IMapper instance if it was not already created, but as in #3, I'm worried this may not be thread safe. Maybe if I did something like this?

public static class MapperConfig
{
    private static IMapper _modelMapper;
    private static readonly object _mapperLocker = new object();

    public static IMapper ModelMapper
    {
        get
        {
            lock(_mapperLocker)
            {
                if (_modelMapper == null)
                {
                    var config = new MapperConfiguration(cfg => cfg.AddProfile(new MappingProfile1()));
                    _modelMapper = config.CreateMapper();
                }
            }

            return _modelMapper;
        }
    }
}

Where two services may call ModelMapper simultaneously. Another downside of this is the first request to any service will have to wait for the mapping to compile, but I'm not sure I can get away from that. I definitely don't want it compiling the mappings per call and would prefer not to even have to do it per service. Can you advise on the thread safety of MapperConfiguration and the best way to use it in IIS-hosted WCF?