I think its absolutely doable with 4k divs if you're fine with T2 crit, T2 AS and T2% phys.
I made this one below 5k divs not accounting locks for 30% quality and corruption. Its 928 dps plus Gain extra mod, so with T2 %phys you will meet your target.
I suppose following strategy: buy 10 exceptional ilvl 80 bases (ilvl 82 just too exensive for your budget). Yolo raise quality to 25-27%. At least 5 bases should survive.
Spam annul + aug on magic bases until got T1 flat phys or T2%phys. Ideally you need T1 flat as it would be much easier to divine final item. Don't try to fracture crit chance on ilvl 80 base - otherwise you will spend all your budget on whittling prefixes.
After spam make items rare with attack speed essence, desecrate prefix, divine to perfect rolls target mod. Fracture, you should get at least 1 out of 5 item ready. Yolo reveal failed fractures, just in case of incredible luck.
Most probably you will continue here with fractured T1 flat phys. Chaos spam T2% phys, add random suffix, use essence of abrasion with cryst omen to convert suffix to third prefix. Prefixes are done.
Add random suffix, convert it to +5 attack skills immediately. Perfect exalt and look for T1-T2 crit. If failed - use essence of abyss and omen of light to remove failed mod. If +5 attack removed - reapply it before exalting again. It should be no more than 50 iterations for T2 crit and 100 for T1 crit. Finally desecrate attack speed. It can be done ultracheap with amanamu omen (max 18% AS), however with current OoL price you can easily spam some 50 desecrations to reveal T2 AS. It took for me 300+ desecrations to reveal T1 AS, however its pretty unlucky.
Edit: ilvl 79 base is also good.
https://preview.redd.it/368gvtluihkg1.png?width=604&format=png&auto=webp&s=fbfa12925f8ab29ac05de342e7acc40849fc292c
