A non ZCD opto triac is able to do phase angle control, not chopping. You can switch on at very time, but not switch off. If you consider how a TRIAC works, you'll surely get the reason. Phase angle control is commonly used for lighting (dimmer). As said, EMC rules require to use full-wave switching for loads other than lamps or motors. You don't need to care for it with a DIY design, but you should for a product.
A SD modulator uses an integrator, but it's not a controller, it doesn't measure a process value, it's just a forward correction scheme. 1st order SD, as usefull in case of a heating fullwave switcher, is a very simple algorithm. You have an accumulator (the integrator) increased by the control value every time step (a fullwave period). If the accumulator value is above a threshold, you switch output for one period and substract a respective value from the accumulator. The error resulting from the 1 bit quantization of the output signal will level over time.