Cuffless blood pressure estimation using the finger-pressing method remains sensitive to improper finger centering and inconsistent contact force, which degrade the accuracy of the oscillometric envelope and PPG signal morphology. This paper details the development of a research prototype that integrates three force sensors and a photoplethysmograph (PPG) sensor to quantify the finger–device interaction. This system is intended as a pre-clinical research tool rather than a clinically validated medical device. We implement a weighted centroid algorithm for center of pressure (CoP) feedback to guide geometric centering, alongside a Hybrid Ridge Regression model to estimate the total contact force. The system was evaluated on a pre-clinical pilot cohort of 48 healthy participants (1274 recordings), comparing inflationary (ramp-up) and deflationary (ramp-down) interaction modalities. Force calibration achieved a mean absolute error (MAE) of 1.2 g, with hardware analysis confirming a limited zero-load baseline drift of −0.29% over 50 days. The best single-recording calibrated model achieved a mean absolute error (MAE) of 5.55 mmHg (systolic) and 5.20 mmHg (diastolic), with a mean error (ME) ± standard deviation (SD) of $+0.50\pm 7.25$ and $+1.19\pm 6.47$ mmHg, respectively, in this pilot cohort, demonstrating the feasibility of the three-point force-sensing design with CoP tracking.