Thanks to help from Nik Rimington and Anders Bjerner, I was able to find a solution utilizing Umbraco's IMediaFileSystem.

Stripped-down example using Dependency Injection:

using Umbraco.Core.IO;
private readonly IMediaFileSystem _mediaFileSystem;
...

// Open a stream for reading the file contents
using (var fs = _mediaFileSystem.OpenFile(mediaUmbracoFile))
{
    if (fs != null)
    {
        var fileTextContent = mediaParser.ParseMediaText(fs,
            out extractedMetaFromTika);
        ...
    }
    else
    {
        _iLogger.Error(typeof(RegisterEventsComponent),
            new Exception($"Unable to open PDF file {fileInfo.FullName}"),
            "Unable to Open PDF file");
    }
}
   ...

public string ParseMediaText(Stream SourceStream, out Dictionary<string, string> MetaData)
{
    var sb = new StringBuilder();
    var metaData = new Dictionary<string, string>();
    var textExtractor = new TextExtractor();
    try
    {
        using (var memoryStream = new MemoryStream())
        {
            SourceStream.CopyTo(memoryStream);
            var streamBytes = memoryStream.ToArray();

            var textExtractionResult = textExtractor.Extract(streamBytes);
            sb.Append(textExtractionResult.Text);
            metaData = (Dictionary<string, string>)textExtractionResult.Metadata;
        }
    }
    catch (Exception ex)
    {
        var msg = $"MediaParserService.ParseMediaText: Could not read media item provided by stream";
        throw new Exception(msg, ex);
    }
    MetaData = metaData;
    return sb.ToString();
}

Additionally, the tip for v9+ implementation is to look at https://github.com/umbraco/UmbracoExamine.PDF/blob/v11/dev/src/UmbracoExamine.PDF/PdfPigTextExtractor.cs