radial engineering has a box for everything when it comes to these types of issues. their boxes are built like tanks and the layouts are very logical. they go up in price as you add features:
https://www.radialeng.com/product_category/reamp
if you already have the hodgepodge cables, try it! either you luck out and it works for you, or it doesn't. if it turns out bad, select the radial box that has the features you need. for example, you already have a high-quality DI input, so you don't need the more expensive radial box that gives you reamp and DI. you would be paying for a DI you don't need.
it is astonishing how nuanced and varied radial's product line is on this topic. guitar gadget boxes are deeply in their product wheelhouse. they are foundational to the company.
the simplest radial reamp box is $99. i would start there if your hodgepodge solution fails. you could buy a few different radial boxes and keep the winner. i don't know what the sound difference is between the $99 reamp hp and the $129 prormp. it gets incredibly nuanced. radial has you covered in all directions. you just need to select the feature set you want.
if you are going to repeat this workflow (track DI, reamp when something good happens) i think it makes sense to get a professional purpose-built box rather than rely on a hodgepodge solution. especially if the professional solution costs as low as $99.