Redirecting static IP traffic to dynamic host
No.
There are a number of partial solutions and answers, but the last sentence - masking your home IP and not routing traffic via VPS without additional resources - is not doable.
Have you considered getting a VPN with a static IP (its a thing, and not uncommon, but a different use case to what most people think of). The cost of this is comparatively low (US$5-US$20 per month) and it ticks your boxes - masks your home IP, does not go through VPS.