Sounds more like a clutch problem. May have nothing to do with engagement point, but rather a sticky or worn/notched spline shaft that is keeping the clutch disk from sliding away from the flywheel. Or, the more likely suspect is a bad pilot bearing - the little $2 bearing in the center of the flywheel that supports the tranny input shaft. When it seizes, the flywheel keeps the tranny shaft spinning even when the clutch is disengaged.

Before you tear out the tranny for the clutch job, change the tranny fluid. Use a good synthetic - I like the AMSOIL syn auto trans fluid, but REDLINE MTL is also reported to work well. And be sure to remove the OD bottom cover to drain that as well (have new gasket available). If the new fluid does not help, or if it is still difficult to get into first from stop without shifting into second or third first, then go for the clutch. Be sure to get the top quality sealed pilot bearing when you do the clutch job, and if the old bearing is seized, be prepared for a nasty job of removing the old one - good quality slide hammer puller is a necessity!

BTW - during your annual or bi-annual brake system flush, be sure to bleed the clutch slave cylinder as well (often overlooked) as it also uses the brake reservoir.