I used to have the same problem
i used to have the same problem playing successive notes with the kick at a similar tempo. i have a few solutions to this. your tempo wise you follow Alvin's advice which is awesome.
1)
relaxation-for the foot control on whether it stunts or gets into a "spasm", what you need to focus on would be to relax while you play the groove. if your muscles tense up there would be no way you can pull it off and your practice is not going to be efficient. you probably would give up after a while due to the tension in your muscles.
2)
short rest in between exercises- I have students who are very ambitious about their practice and they rush towards their goals by continuously practicing certain exercises without short periods of rest in between. practicing this way tenses up your muscles really fast and it would be difficult to move up the metronome during the same practice session if you are not practicing efficiently. a rule of thumb that you can choose to follow for short exercises would be to continuously play the exercise for a minute and rest for 30 seconds and then continue the exercise again until you can comfortably play it at a certain tempo and then increase the tempo about 4 or 5 bpm like what Alvin said.
3)
Count out aloud-counting while playing really help even out the exercise ensuring you are playing the subdivisions evenly. depending on the tempo, for example at 70 bpm you can play the whole groove while counting semiquavers or 16th notes aloud while the metronome is clicking crotchets. e.g. 1ena 2ena 3ena 4ena
4)
Head room-If you ever noticed. a lot of the greatest drummers in the world can play very fast and they make it seem very effortless on their faces. many drummers i have seen can play fast but with so much agony on their faces and they can really sweat it out. the difference would be the concept of practicing with headroom. if you want to play this groove at 70bpm effortlessly or at least comfortably so to speak, you need to practice it at tempos beyond 70 bpm. one idea that i put across to my students would be to play it four "steps" higher than the tempo you are aiming for. i like to use the word "steps" which means each step would be an increase in 4 bpm. what i would do is to practice exercises four steps higher than my goal. for example, if i want to play at 70bpm comfortably, i practice the exercise at 70,74,78,82, and 86 bpm. most of of the time when you reach the highest "step", your muscles start tensing up. when this happens, stop immediately and rest for a 30 seconds or so and start again. i usually practice my starting tempo 8 "steps" below my goal. the most important thing to remember would be to start slow and build your exercise up to speed. the slower tempos warm your muscles up to be able to handle the faster tempos.
5)
Seat height-this would be subjective to different drummers because some like to sit low and some like to sit high. Steve Gadd for example sits low and his kick drum techniques are more tap dance related(he used to tap dance btw) compared to Thomas Lang who sits high giving him a greater advantage to pull off fast double strokes with his pedals. so experiment with your seat height to see which gives you more control over the foot pedal and doesn't give you spasms or stunts. for me i used to sit low and that gave me problems with my foot control, when i increased the seat height, i had more control over the pedal which made playing of successive notes with a single pedal much easier than before.
these are a few solutions that helped me solve the problem that you are currently having and these are solutions that i provide my students who come back with such problems so try them out