I’m not a kid’s teacher so I can’t suggest specific materials. You’re right that the grammar focus is ingrained here to the point of being stultifying. It sounds like your using a PPP methodology which tends to focus on practising some grammatical rule in contrived situations. This approach is great for teachers but not so for learners. It’s also non-representative; Most of us didn’t learn grammar, if at all, until we were adults.
Try getting your kids involved in some meaningful task where there is a goal which will allow practise of some of the grammar you have taught. But make the task goal the objective, not the parroting of taught grammar. This is far more natural and will likely cover a range of tenses in a natural presentation.
Tasks should be well specified so that you can preteach any likely required vocabulary or structures. They should also involve group work during which time the students use any language resources they have to get to the goal. Don’t enforce English only here.
In the last stage, students report back their results to the class and it is here only that you focus on accuracy. This allows consolidation.
I use this approach all the time with adults and it is well received. If you make your tasks (1) interesting and (2) tailored as much as possible to the expressive needs of your students, they will get a lot out of them.