You don't need archery at 100%.
- Go to Riften, keep asking Ungrien about maven, and get speech up to 100%. Inbetween levelling up, train light armour with the Grelka in the square.
- Once speech is very high, make weapons at a forge. Inbetween leveling smithing, keep fast travelling to Winterhold to train in Destruction and Restoration.
- Once you've smithed tonnes of stuff, enchant it all, and get enchanting up. Bear in mind enchanting goes up for the number of items enchanted, NOT the strength of the item.
- Invest in the riverwood trader. You can sell enchanted items for big money if your speech is high as per (1), then go back to whiterun to buy ingots to make more stuff.
Then you can enchant bows without the need to have archery at 100%. Double enchanted bows with fire and ice are very powerful. You can also enchant clothes so destruction and restoration cost you no magika, making your character a fairly armed to the teeth mage with good arrow skills and good light armour resistance for out in the field.