Redraw Corporate Logo for Vector Production

I need our corporate logo redrawn as a clean, production-ready vector file. The original master file has been lost and I only have a JPG and a poor auto-traced SVG (which contains thousands of fragmented paths from JPG compression artefacts — not usable).
Deliverables:

Master vector file in Adobe Illustrator (.ai) format, fully editable, with named layers
EPS and PDF versions
SVG optimised for web use
PNG exports with transparent background at 500px, 1000px, and 2000px wide
Both full-colour and single-colour (black, white) versions

Requirements:

Logo must be redrawn from scratch using proper vector paths (not auto-traced)
Clean Bézier curves, minimal anchor points, mathematically accurate geometry
Colours specified in both RGB (screen) and CMYK (print) — exact values to be matched from source and confirmed with me
Typography: identify the font used in the wordmark; if commercial, convert to outlines and note the font name for our records
Provide a simple brand sheet (1-page PDF) showing logo variations, clear space, minimum sizes, and colour values

Source material I'll provide:

High-resolution JPG of current logo
The auto-traced SVG (for reference only — do not use as a base)