I have a very weedy lawn and I’m wondering whether to reseed or smother the weeds with a tarp and start over again with new seed.
To renovate the existing lawn, use corn gluten in the spring when the forsythia appears. Wait 6 weeks before reseeding as the gluten will inhibit the germination of lawn seed as well as weeds. One disadvantage with this approach is that you will probably be reseeding closer to summertime when it is may be hotter.
The other option you asked about was to smother the existing lawn with tarp. This can be done now (mid-April). You will need to leave the tarp for about 3 months. Then seed the lawn area in the fall.
Buy a seed mix from a reputable nursery. You mentioned that your existing lawn had fescues, ryegrass and some bluegrass. Fescues are slow growing. The ryegrass in the mix grows more quickly and acts as a filler until the fescues get established. Reseeding on an ongoing basis may be necessary.
Lawn grasses respond best between 5.5 and 7.5. Consider applying lime if your soil is too acidic or a sulphur treatment if it is too alkaline. Weeds often grow best in acidic soil.